$(x+y)^n$の展開式のリスト
$(x+y)^{2}$から$(x+y)^{50}$までの展開の結果を以下に示します。係数はすべて二項係数${}_{n}\mathrm{C}_{k}$なので、あまり有難いリストではありません。
(x + y)^{2} = x^{2} + 2 x y + y^{2}
(x + y)^{3} = x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3}
(x + y)^{4} = x^{4} + 4 x^{3} y + 6 x^{2} y^{2} + 4 x y^{3} + y^{4}
(x + y)^{5} = x^{5} + 5 x^{4} y + 10 x^{3} y^{2} + 10 x^{2} y^{3} + 5 x y^{4} + y^{5}
(x + y)^{6} = x^{6} + 6 x^{5} y + 15 x^{4} y^{2} + 20 x^{3} y^{3} + 15 x^{2} y^{4} + 6 x y^{5} + y^{6}
(x + y)^{7} = x^{7} + 7 x^{6} y + 21 x^{5} y^{2} + 35 x^{4} y^{3} + 35 x^{3} y^{4} + 21 x^{2} y^{5} + 7 x y^{6} + y^{7}
(x + y)^{8} = x^{8} + 8 x^{7} y + 28 x^{6} y^{2} + 56 x^{5} y^{3} + 70 x^{4} y^{4} + 56 x^{3} y^{5} + 28 x^{2} y^{6} + 8 x y^{7} + y^{8}
(x + y)^{9} = x^{9} + 9 x^{8} y + 36 x^{7} y^{2} + 84 x^{6} y^{3} + 126 x^{5} y^{4} + 126 x^{4} y^{5} + 84 x^{3} y^{6} + 36 x^{2} y^{7} + 9 x y^{8} + y^{9}
(x + y)^{10} = x^{10} + 10 x^{9} y + 45 x^{8} y^{2} + 120 x^{7} y^{3} + 210 x^{6} y^{4} + 252 x^{5} y^{5} + 210 x^{4} y^{6} + 120 x^{3} y^{7} + 45 x^{2} y^{8} + 10 x y^{9} + y^{10}
(x + y)^{11} = x^{11} + 11 x^{10} y + 55 x^{9} y^{2} + 165 x^{8} y^{3} + 330 x^{7} y^{4} + 462 x^{6} y^{5} + 462 x^{5} y^{6} + 330 x^{4} y^{7} + 165 x^{3} y^{8} + 55 x^{2} y^{9} + 11 x y^{10} + y^{11}
(x + y)^{12} = x^{12} + 12 x^{11} y + 66 x^{10} y^{2} + 220 x^{9} y^{3} + 495 x^{8} y^{4} + 792 x^{7} y^{5} + 924 x^{6} y^{6} + 792 x^{5} y^{7} + 495 x^{4} y^{8} + 220 x^{3} y^{9} + 66 x^{2} y^{10} + 12 x y^{11} + y^{12}
(x + y)^{13} = x^{13} + 13 x^{12} y + 78 x^{11} y^{2} + 286 x^{10} y^{3} + 715 x^{9} y^{4} + 1287 x^{8} y^{5} + 1716 x^{7} y^{6} + 1716 x^{6} y^{7} + 1287 x^{5} y^{8} + 715 x^{4} y^{9} + 286 x^{3} y^{10} + 78 x^{2} y^{11} + 13 x y^{12} + y^{13}
(x + y)^{14} = x^{14} + 14 x^{13} y + 91 x^{12} y^{2} + 364 x^{11} y^{3} + 1001 x^{10} y^{4} + 2002 x^{9} y^{5} + 3003 x^{8} y^{6} + 3432 x^{7} y^{7} + 3003 x^{6} y^{8} + 2002 x^{5} y^{9} + 1001 x^{4} y^{10} + 364 x^{3} y^{11} + 91 x^{2} y^{12} + 14 x y^{13} + y^{14}
(x + y)^{15} = x^{15} + 15 x^{14} y + 105 x^{13} y^{2} + 455 x^{12} y^{3} + 1365 x^{11} y^{4} + 3003 x^{10} y^{5} + 5005 x^{9} y^{6} + 6435 x^{8} y^{7} + 6435 x^{7} y^{8} + 5005 x^{6} y^{9} + 3003 x^{5} y^{10} + 1365 x^{4} y^{11} + 455 x^{3} y^{12} + 105 x^{2} y^{13} + 15 x y^{14} + y^{15}
(x + y)^{16} = x^{16} + 16 x^{15} y + 120 x^{14} y^{2} + 560 x^{13} y^{3} + 1820 x^{12} y^{4} + 4368 x^{11} y^{5} + 8008 x^{10} y^{6} + 11440 x^{9} y^{7} + 12870 x^{8} y^{8} + 11440 x^{7} y^{9} + 8008 x^{6} y^{10} + 4368 x^{5} y^{11} + 1820 x^{4} y^{12} + 560 x^{3} y^{13} + 120 x^{2} y^{14} + 16 x y^{15} + y^{16}
(x + y)^{17} = x^{17} + 17 x^{16} y + 136 x^{15} y^{2} + 680 x^{14} y^{3} + 2380 x^{13} y^{4} + 6188 x^{12} y^{5} + 12376 x^{11} y^{6} + 19448 x^{10} y^{7} + 24310 x^{9} y^{8} + 24310 x^{8} y^{9} + 19448 x^{7} y^{10} + 12376 x^{6} y^{11} + 6188 x^{5} y^{12} + 2380 x^{4} y^{13} + 680 x^{3} y^{14} + 136 x^{2} y^{15} + 17 x y^{16} + y^{17}
(x + y)^{18} = x^{18} + 18 x^{17} y + 153 x^{16} y^{2} + 816 x^{15} y^{3} + 3060 x^{14} y^{4} + 8568 x^{13} y^{5} + 18564 x^{12} y^{6} + 31824 x^{11} y^{7} + 43758 x^{10} y^{8} + 48620 x^{9} y^{9} + 43758 x^{8} y^{10} + 31824 x^{7} y^{11} + 18564 x^{6} y^{12} + 8568 x^{5} y^{13} + 3060 x^{4} y^{14} + 816 x^{3} y^{15} + 153 x^{2} y^{16} + 18 x y^{17} + y^{18}
(x + y)^{19} = x^{19} + 19 x^{18} y + 171 x^{17} y^{2} + 969 x^{16} y^{3} + 3876 x^{15} y^{4} + 11628 x^{14} y^{5} + 27132 x^{13} y^{6} + 50388 x^{12} y^{7} + 75582 x^{11} y^{8} + 92378 x^{10} y^{9} + 92378 x^{9} y^{10} + 75582 x^{8} y^{11} + 50388 x^{7} y^{12} + 27132 x^{6} y^{13} + 11628 x^{5} y^{14} + 3876 x^{4} y^{15} + 969 x^{3} y^{16} + 171 x^{2} y^{17} + 19 x y^{18} + y^{19}
(x + y)^{20} = x^{20} + 20 x^{19} y + 190 x^{18} y^{2} + 1140 x^{17} y^{3} + 4845 x^{16} y^{4} + 15504 x^{15} y^{5} + 38760 x^{14} y^{6} + 77520 x^{13} y^{7} + 125970 x^{12} y^{8} + 167960 x^{11} y^{9} + 184756 x^{10} y^{10} + 167960 x^{9} y^{11} + 125970 x^{8} y^{12} + 77520 x^{7} y^{13} + 38760 x^{6} y^{14} + 15504 x^{5} y^{15} + 4845 x^{4} y^{16} + 1140 x^{3} y^{17} + 190 x^{2} y^{18} + 20 x y^{19} + y^{20}
(x + y)^{21} = x^{21} + 21 x^{20} y + 210 x^{19} y^{2} + 1330 x^{18} y^{3} + 5985 x^{17} y^{4} + 20349 x^{16} y^{5} + 54264 x^{15} y^{6} + 116280 x^{14} y^{7} + 203490 x^{13} y^{8} + 293930 x^{12} y^{9} + 352716 x^{11} y^{10} + 352716 x^{10} y^{11} + 293930 x^{9} y^{12} + 203490 x^{8} y^{13} + 116280 x^{7} y^{14} + 54264 x^{6} y^{15} + 20349 x^{5} y^{16} + 5985 x^{4} y^{17} + 1330 x^{3} y^{18} + 210 x^{2} y^{19} + 21 x y^{20} + y^{21}
(x + y)^{22} = x^{22} + 22 x^{21} y + 231 x^{20} y^{2} + 1540 x^{19} y^{3} + 7315 x^{18} y^{4} + 26334 x^{17} y^{5} + 74613 x^{16} y^{6} + 170544 x^{15} y^{7} + 319770 x^{14} y^{8} + 497420 x^{13} y^{9} + 646646 x^{12} y^{10} + 705432 x^{11} y^{11} + 646646 x^{10} y^{12} + 497420 x^{9} y^{13} + 319770 x^{8} y^{14} + 170544 x^{7} y^{15} + 74613 x^{6} y^{16} + 26334 x^{5} y^{17} + 7315 x^{4} y^{18} + 1540 x^{3} y^{19} + 231 x^{2} y^{20} + 22 x y^{21} + y^{22}
(x + y)^{23} = x^{23} + 23 x^{22} y + 253 x^{21} y^{2} + 1771 x^{20} y^{3} + 8855 x^{19} y^{4} + 33649 x^{18} y^{5} + 100947 x^{17} y^{6} + 245157 x^{16} y^{7} + 490314 x^{15} y^{8} + 817190 x^{14} y^{9} + 1144066 x^{13} y^{10} + 1352078 x^{12} y^{11} + 1352078 x^{11} y^{12} + 1144066 x^{10} y^{13} + 817190 x^{9} y^{14} + 490314 x^{8} y^{15} + 245157 x^{7} y^{16} + 100947 x^{6} y^{17} + 33649 x^{5} y^{18} + 8855 x^{4} y^{19} + 1771 x^{3} y^{20} + 253 x^{2} y^{21} + 23 x y^{22} + y^{23}
(x + y)^{24} = x^{24} + 24 x^{23} y + 276 x^{22} y^{2} + 2024 x^{21} y^{3} + 10626 x^{20} y^{4} + 42504 x^{19} y^{5} + 134596 x^{18} y^{6} + 346104 x^{17} y^{7} + 735471 x^{16} y^{8} + 1307504 x^{15} y^{9} + 1961256 x^{14} y^{10} + 2496144 x^{13} y^{11} + 2704156 x^{12} y^{12} + 2496144 x^{11} y^{13} + 1961256 x^{10} y^{14} + 1307504 x^{9} y^{15} + 735471 x^{8} y^{16} + 346104 x^{7} y^{17} + 134596 x^{6} y^{18} + 42504 x^{5} y^{19} + 10626 x^{4} y^{20} + 2024 x^{3} y^{21} + 276 x^{2} y^{22} + 24 x y^{23} + y^{24}
(x + y)^{25} = x^{25} + 25 x^{24} y + 300 x^{23} y^{2} + 2300 x^{22} y^{3} + 12650 x^{21} y^{4} + 53130 x^{20} y^{5} + 177100 x^{19} y^{6} + 480700 x^{18} y^{7} + 1081575 x^{17} y^{8} + 2042975 x^{16} y^{9} + 3268760 x^{15} y^{10} + 4457400 x^{14} y^{11} + 5200300 x^{13} y^{12} + 5200300 x^{12} y^{13} + 4457400 x^{11} y^{14} + 3268760 x^{10} y^{15} + 2042975 x^{9} y^{16} + 1081575 x^{8} y^{17} + 480700 x^{7} y^{18} + 177100 x^{6} y^{19} + 53130 x^{5} y^{20} + 12650 x^{4} y^{21} + 2300 x^{3} y^{22} + 300 x^{2} y^{23} + 25 x y^{24} + y^{25}
(x + y)^{26} = x^{26} + 26 x^{25} y + 325 x^{24} y^{2} + 2600 x^{23} y^{3} + 14950 x^{22} y^{4} + 65780 x^{21} y^{5} + 230230 x^{20} y^{6} + 657800 x^{19} y^{7} + 1562275 x^{18} y^{8} + 3124550 x^{17} y^{9} + 5311735 x^{16} y^{10} + 7726160 x^{15} y^{11} + 9657700 x^{14} y^{12} + 10400600 x^{13} y^{13} + 9657700 x^{12} y^{14} + 7726160 x^{11} y^{15} + 5311735 x^{10} y^{16} + 3124550 x^{9} y^{17} + 1562275 x^{8} y^{18} + 657800 x^{7} y^{19} + 230230 x^{6} y^{20} + 65780 x^{5} y^{21} + 14950 x^{4} y^{22} + 2600 x^{3} y^{23} + 325 x^{2} y^{24} + 26 x y^{25} + y^{26}
(x + y)^{27} = x^{27} + 27 x^{26} y + 351 x^{25} y^{2} + 2925 x^{24} y^{3} + 17550 x^{23} y^{4} + 80730 x^{22} y^{5} + 296010 x^{21} y^{6} + 888030 x^{20} y^{7} + 2220075 x^{19} y^{8} + 4686825 x^{18} y^{9} + 8436285 x^{17} y^{10} + 13037895 x^{16} y^{11} + 17383860 x^{15} y^{12} + 20058300 x^{14} y^{13} + 20058300 x^{13} y^{14} + 17383860 x^{12} y^{15} + 13037895 x^{11} y^{16} + 8436285 x^{10} y^{17} + 4686825 x^{9} y^{18} + 2220075 x^{8} y^{19} + 888030 x^{7} y^{20} + 296010 x^{6} y^{21} + 80730 x^{5} y^{22} + 17550 x^{4} y^{23} + 2925 x^{3} y^{24} + 351 x^{2} y^{25} + 27 x y^{26} + y^{27}
(x + y)^{28} = x^{28} + 28 x^{27} y + 378 x^{26} y^{2} + 3276 x^{25} y^{3} + 20475 x^{24} y^{4} + 98280 x^{23} y^{5} + 376740 x^{22} y^{6} + 1184040 x^{21} y^{7} + 3108105 x^{20} y^{8} + 6906900 x^{19} y^{9} + 13123110 x^{18} y^{10} + 21474180 x^{17} y^{11} + 30421755 x^{16} y^{12} + 37442160 x^{15} y^{13} + 40116600 x^{14} y^{14} + 37442160 x^{13} y^{15} + 30421755 x^{12} y^{16} + 21474180 x^{11} y^{17} + 13123110 x^{10} y^{18} + 6906900 x^{9} y^{19} + 3108105 x^{8} y^{20} + 1184040 x^{7} y^{21} + 376740 x^{6} y^{22} + 98280 x^{5} y^{23} + 20475 x^{4} y^{24} + 3276 x^{3} y^{25} + 378 x^{2} y^{26} + 28 x y^{27} + y^{28}
(x + y)^{29} = x^{29} + 29 x^{28} y + 406 x^{27} y^{2} + 3654 x^{26} y^{3} + 23751 x^{25} y^{4} + 118755 x^{24} y^{5} + 475020 x^{23} y^{6} + 1560780 x^{22} y^{7} + 4292145 x^{21} y^{8} + 10015005 x^{20} y^{9} + 20030010 x^{19} y^{10} + 34597290 x^{18} y^{11} + 51895935 x^{17} y^{12} + 67863915 x^{16} y^{13} + 77558760 x^{15} y^{14} + 77558760 x^{14} y^{15} + 67863915 x^{13} y^{16} + 51895935 x^{12} y^{17} + 34597290 x^{11} y^{18} + 20030010 x^{10} y^{19} + 10015005 x^{9} y^{20} + 4292145 x^{8} y^{21} + 1560780 x^{7} y^{22} + 475020 x^{6} y^{23} + 118755 x^{5} y^{24} + 23751 x^{4} y^{25} + 3654 x^{3} y^{26} + 406 x^{2} y^{27} + 29 x y^{28} + y^{29}
(x + y)^{30} = x^{30} + 30 x^{29} y + 435 x^{28} y^{2} + 4060 x^{27} y^{3} + 27405 x^{26} y^{4} + 142506 x^{25} y^{5} + 593775 x^{24} y^{6} + 2035800 x^{23} y^{7} + 5852925 x^{22} y^{8} + 14307150 x^{21} y^{9} + 30045015 x^{20} y^{10} + 54627300 x^{19} y^{11} + 86493225 x^{18} y^{12} + 119759850 x^{17} y^{13} + 145422675 x^{16} y^{14} + 155117520 x^{15} y^{15} + 145422675 x^{14} y^{16} + 119759850 x^{13} y^{17} + 86493225 x^{12} y^{18} + 54627300 x^{11} y^{19} + 30045015 x^{10} y^{20} + 14307150 x^{9} y^{21} + 5852925 x^{8} y^{22} + 2035800 x^{7} y^{23} + 593775 x^{6} y^{24} + 142506 x^{5} y^{25} + 27405 x^{4} y^{26} + 4060 x^{3} y^{27} + 435 x^{2} y^{28} + 30 x y^{29} + y^{30}
(x + y)^{31} = x^{31} + 31 x^{30} y + 465 x^{29} y^{2} + 4495 x^{28} y^{3} + 31465 x^{27} y^{4} + 169911 x^{26} y^{5} + 736281 x^{25} y^{6} + 2629575 x^{24} y^{7} + 7888725 x^{23} y^{8} + 20160075 x^{22} y^{9} + 44352165 x^{21} y^{10} + 84672315 x^{20} y^{11} + 141120525 x^{19} y^{12} + 206253075 x^{18} y^{13} + 265182525 x^{17} y^{14} + 300540195 x^{16} y^{15} + 300540195 x^{15} y^{16} + 265182525 x^{14} y^{17} + 206253075 x^{13} y^{18} + 141120525 x^{12} y^{19} + 84672315 x^{11} y^{20} + 44352165 x^{10} y^{21} + 20160075 x^{9} y^{22} + 7888725 x^{8} y^{23} + 2629575 x^{7} y^{24} + 736281 x^{6} y^{25} + 169911 x^{5} y^{26} + 31465 x^{4} y^{27} + 4495 x^{3} y^{28} + 465 x^{2} y^{29} + 31 x y^{30} + y^{31}
(x + y)^{32} = x^{32} + 32 x^{31} y + 496 x^{30} y^{2} + 4960 x^{29} y^{3} + 35960 x^{28} y^{4} + 201376 x^{27} y^{5} + 906192 x^{26} y^{6} + 3365856 x^{25} y^{7} + 10518300 x^{24} y^{8} + 28048800 x^{23} y^{9} + 64512240 x^{22} y^{10} + 129024480 x^{21} y^{11} + 225792840 x^{20} y^{12} + 347373600 x^{19} y^{13} + 471435600 x^{18} y^{14} + 565722720 x^{17} y^{15} + 601080390 x^{16} y^{16} + 565722720 x^{15} y^{17} + 471435600 x^{14} y^{18} + 347373600 x^{13} y^{19} + 225792840 x^{12} y^{20} + 129024480 x^{11} y^{21} + 64512240 x^{10} y^{22} + 28048800 x^{9} y^{23} + 10518300 x^{8} y^{24} + 3365856 x^{7} y^{25} + 906192 x^{6} y^{26} + 201376 x^{5} y^{27} + 35960 x^{4} y^{28} + 4960 x^{3} y^{29} + 496 x^{2} y^{30} + 32 x y^{31} + y^{32}
(x + y)^{33} = x^{33} + 33 x^{32} y + 528 x^{31} y^{2} + 5456 x^{30} y^{3} + 40920 x^{29} y^{4} + 237336 x^{28} y^{5} + 1107568 x^{27} y^{6} + 4272048 x^{26} y^{7} + 13884156 x^{25} y^{8} + 38567100 x^{24} y^{9} + 92561040 x^{23} y^{10} + 193536720 x^{22} y^{11} + 354817320 x^{21} y^{12} + 573166440 x^{20} y^{13} + 818809200 x^{19} y^{14} + 1037158320 x^{18} y^{15} + 1166803110 x^{17} y^{16} + 1166803110 x^{16} y^{17} + 1037158320 x^{15} y^{18} + 818809200 x^{14} y^{19} + 573166440 x^{13} y^{20} + 354817320 x^{12} y^{21} + 193536720 x^{11} y^{22} + 92561040 x^{10} y^{23} + 38567100 x^{9} y^{24} + 13884156 x^{8} y^{25} + 4272048 x^{7} y^{26} + 1107568 x^{6} y^{27} + 237336 x^{5} y^{28} + 40920 x^{4} y^{29} + 5456 x^{3} y^{30} + 528 x^{2} y^{31} + 33 x y^{32} + y^{33}
(x + y)^{34} = x^{34} + 34 x^{33} y + 561 x^{32} y^{2} + 5984 x^{31} y^{3} + 46376 x^{30} y^{4} + 278256 x^{29} y^{5} + 1344904 x^{28} y^{6} + 5379616 x^{27} y^{7} + 18156204 x^{26} y^{8} + 52451256 x^{25} y^{9} + 131128140 x^{24} y^{10} + 286097760 x^{23} y^{11} + 548354040 x^{22} y^{12} + 927983760 x^{21} y^{13} + 1391975640 x^{20} y^{14} + 1855967520 x^{19} y^{15} + 2203961430 x^{18} y^{16} + 2333606220 x^{17} y^{17} + 2203961430 x^{16} y^{18} + 1855967520 x^{15} y^{19} + 1391975640 x^{14} y^{20} + 927983760 x^{13} y^{21} + 548354040 x^{12} y^{22} + 286097760 x^{11} y^{23} + 131128140 x^{10} y^{24} + 52451256 x^{9} y^{25} + 18156204 x^{8} y^{26} + 5379616 x^{7} y^{27} + 1344904 x^{6} y^{28} + 278256 x^{5} y^{29} + 46376 x^{4} y^{30} + 5984 x^{3} y^{31} + 561 x^{2} y^{32} + 34 x y^{33} + y^{34}
(x + y)^{35} = x^{35} + 35 x^{34} y + 595 x^{33} y^{2} + 6545 x^{32} y^{3} + 52360 x^{31} y^{4} + 324632 x^{30} y^{5} + 1623160 x^{29} y^{6} + 6724520 x^{28} y^{7} + 23535820 x^{27} y^{8} + 70607460 x^{26} y^{9} + 183579396 x^{25} y^{10} + 417225900 x^{24} y^{11} + 834451800 x^{23} y^{12} + 1476337800 x^{22} y^{13} + 2319959400 x^{21} y^{14} + 3247943160 x^{20} y^{15} + 4059928950 x^{19} y^{16} + 4537567650 x^{18} y^{17} + 4537567650 x^{17} y^{18} + 4059928950 x^{16} y^{19} + 3247943160 x^{15} y^{20} + 2319959400 x^{14} y^{21} + 1476337800 x^{13} y^{22} + 834451800 x^{12} y^{23} + 417225900 x^{11} y^{24} + 183579396 x^{10} y^{25} + 70607460 x^{9} y^{26} + 23535820 x^{8} y^{27} + 6724520 x^{7} y^{28} + 1623160 x^{6} y^{29} + 324632 x^{5} y^{30} + 52360 x^{4} y^{31} + 6545 x^{3} y^{32} + 595 x^{2} y^{33} + 35 x y^{34} + y^{35}
(x + y)^{36} = x^{36} + 36 x^{35} y + 630 x^{34} y^{2} + 7140 x^{33} y^{3} + 58905 x^{32} y^{4} + 376992 x^{31} y^{5} + 1947792 x^{30} y^{6} + 8347680 x^{29} y^{7} + 30260340 x^{28} y^{8} + 94143280 x^{27} y^{9} + 254186856 x^{26} y^{10} + 600805296 x^{25} y^{11} + 1251677700 x^{24} y^{12} + 2310789600 x^{23} y^{13} + 3796297200 x^{22} y^{14} + 5567902560 x^{21} y^{15} + 7307872110 x^{20} y^{16} + 8597496600 x^{19} y^{17} + 9075135300 x^{18} y^{18} + 8597496600 x^{17} y^{19} + 7307872110 x^{16} y^{20} + 5567902560 x^{15} y^{21} + 3796297200 x^{14} y^{22} + 2310789600 x^{13} y^{23} + 1251677700 x^{12} y^{24} + 600805296 x^{11} y^{25} + 254186856 x^{10} y^{26} + 94143280 x^{9} y^{27} + 30260340 x^{8} y^{28} + 8347680 x^{7} y^{29} + 1947792 x^{6} y^{30} + 376992 x^{5} y^{31} + 58905 x^{4} y^{32} + 7140 x^{3} y^{33} + 630 x^{2} y^{34} + 36 x y^{35} + y^{36}
(x + y)^{37} = x^{37} + 37 x^{36} y + 666 x^{35} y^{2} + 7770 x^{34} y^{3} + 66045 x^{33} y^{4} + 435897 x^{32} y^{5} + 2324784 x^{31} y^{6} + 10295472 x^{30} y^{7} + 38608020 x^{29} y^{8} + 124403620 x^{28} y^{9} + 348330136 x^{27} y^{10} + 854992152 x^{26} y^{11} + 1852482996 x^{25} y^{12} + 3562467300 x^{24} y^{13} + 6107086800 x^{23} y^{14} + 9364199760 x^{22} y^{15} + 12875774670 x^{21} y^{16} + 15905368710 x^{20} y^{17} + 17672631900 x^{19} y^{18} + 17672631900 x^{18} y^{19} + 15905368710 x^{17} y^{20} + 12875774670 x^{16} y^{21} + 9364199760 x^{15} y^{22} + 6107086800 x^{14} y^{23} + 3562467300 x^{13} y^{24} + 1852482996 x^{12} y^{25} + 854992152 x^{11} y^{26} + 348330136 x^{10} y^{27} + 124403620 x^{9} y^{28} + 38608020 x^{8} y^{29} + 10295472 x^{7} y^{30} + 2324784 x^{6} y^{31} + 435897 x^{5} y^{32} + 66045 x^{4} y^{33} + 7770 x^{3} y^{34} + 666 x^{2} y^{35} + 37 x y^{36} + y^{37}
(x + y)^{38} = x^{38} + 38 x^{37} y + 703 x^{36} y^{2} + 8436 x^{35} y^{3} + 73815 x^{34} y^{4} + 501942 x^{33} y^{5} + 2760681 x^{32} y^{6} + 12620256 x^{31} y^{7} + 48903492 x^{30} y^{8} + 163011640 x^{29} y^{9} + 472733756 x^{28} y^{10} + 1203322288 x^{27} y^{11} + 2707475148 x^{26} y^{12} + 5414950296 x^{25} y^{13} + 9669554100 x^{24} y^{14} + 15471286560 x^{23} y^{15} + 22239974430 x^{22} y^{16} + 28781143380 x^{21} y^{17} + 33578000610 x^{20} y^{18} + 35345263800 x^{19} y^{19} + 33578000610 x^{18} y^{20} + 28781143380 x^{17} y^{21} + 22239974430 x^{16} y^{22} + 15471286560 x^{15} y^{23} + 9669554100 x^{14} y^{24} + 5414950296 x^{13} y^{25} + 2707475148 x^{12} y^{26} + 1203322288 x^{11} y^{27} + 472733756 x^{10} y^{28} + 163011640 x^{9} y^{29} + 48903492 x^{8} y^{30} + 12620256 x^{7} y^{31} + 2760681 x^{6} y^{32} + 501942 x^{5} y^{33} + 73815 x^{4} y^{34} + 8436 x^{3} y^{35} + 703 x^{2} y^{36} + 38 x y^{37} + y^{38}
(x + y)^{39} = x^{39} + 39 x^{38} y + 741 x^{37} y^{2} + 9139 x^{36} y^{3} + 82251 x^{35} y^{4} + 575757 x^{34} y^{5} + 3262623 x^{33} y^{6} + 15380937 x^{32} y^{7} + 61523748 x^{31} y^{8} + 211915132 x^{30} y^{9} + 635745396 x^{29} y^{10} + 1676056044 x^{28} y^{11} + 3910797436 x^{27} y^{12} + 8122425444 x^{26} y^{13} + 15084504396 x^{25} y^{14} + 25140840660 x^{24} y^{15} + 37711260990 x^{23} y^{16} + 51021117810 x^{22} y^{17} + 62359143990 x^{21} y^{18} + 68923264410 x^{20} y^{19} + 68923264410 x^{19} y^{20} + 62359143990 x^{18} y^{21} + 51021117810 x^{17} y^{22} + 37711260990 x^{16} y^{23} + 25140840660 x^{15} y^{24} + 15084504396 x^{14} y^{25} + 8122425444 x^{13} y^{26} + 3910797436 x^{12} y^{27} + 1676056044 x^{11} y^{28} + 635745396 x^{10} y^{29} + 211915132 x^{9} y^{30} + 61523748 x^{8} y^{31} + 15380937 x^{7} y^{32} + 3262623 x^{6} y^{33} + 575757 x^{5} y^{34} + 82251 x^{4} y^{35} + 9139 x^{3} y^{36} + 741 x^{2} y^{37} + 39 x y^{38} + y^{39}
(x + y)^{40} = x^{40} + 40 x^{39} y + 780 x^{38} y^{2} + 9880 x^{37} y^{3} + 91390 x^{36} y^{4} + 658008 x^{35} y^{5} + 3838380 x^{34} y^{6} + 18643560 x^{33} y^{7} + 76904685 x^{32} y^{8} + 273438880 x^{31} y^{9} + 847660528 x^{30} y^{10} + 2311801440 x^{29} y^{11} + 5586853480 x^{28} y^{12} + 12033222880 x^{27} y^{13} + 23206929840 x^{26} y^{14} + 40225345056 x^{25} y^{15} + 62852101650 x^{24} y^{16} + 88732378800 x^{23} y^{17} + 113380261800 x^{22} y^{18} + 131282408400 x^{21} y^{19} + 137846528820 x^{20} y^{20} + 131282408400 x^{19} y^{21} + 113380261800 x^{18} y^{22} + 88732378800 x^{17} y^{23} + 62852101650 x^{16} y^{24} + 40225345056 x^{15} y^{25} + 23206929840 x^{14} y^{26} + 12033222880 x^{13} y^{27} + 5586853480 x^{12} y^{28} + 2311801440 x^{11} y^{29} + 847660528 x^{10} y^{30} + 273438880 x^{9} y^{31} + 76904685 x^{8} y^{32} + 18643560 x^{7} y^{33} + 3838380 x^{6} y^{34} + 658008 x^{5} y^{35} + 91390 x^{4} y^{36} + 9880 x^{3} y^{37} + 780 x^{2} y^{38} + 40 x y^{39} + y^{40}
(x + y)^{41} = x^{41} + 41 x^{40} y + 820 x^{39} y^{2} + 10660 x^{38} y^{3} + 101270 x^{37} y^{4} + 749398 x^{36} y^{5} + 4496388 x^{35} y^{6} + 22481940 x^{34} y^{7} + 95548245 x^{33} y^{8} + 350343565 x^{32} y^{9} + 1121099408 x^{31} y^{10} + 3159461968 x^{30} y^{11} + 7898654920 x^{29} y^{12} + 17620076360 x^{28} y^{13} + 35240152720 x^{27} y^{14} + 63432274896 x^{26} y^{15} + 103077446706 x^{25} y^{16} + 151584480450 x^{24} y^{17} + 202112640600 x^{23} y^{18} + 244662670200 x^{22} y^{19} + 269128937220 x^{21} y^{20} + 269128937220 x^{20} y^{21} + 244662670200 x^{19} y^{22} + 202112640600 x^{18} y^{23} + 151584480450 x^{17} y^{24} + 103077446706 x^{16} y^{25} + 63432274896 x^{15} y^{26} + 35240152720 x^{14} y^{27} + 17620076360 x^{13} y^{28} + 7898654920 x^{12} y^{29} + 3159461968 x^{11} y^{30} + 1121099408 x^{10} y^{31} + 350343565 x^{9} y^{32} + 95548245 x^{8} y^{33} + 22481940 x^{7} y^{34} + 4496388 x^{6} y^{35} + 749398 x^{5} y^{36} + 101270 x^{4} y^{37} + 10660 x^{3} y^{38} + 820 x^{2} y^{39} + 41 x y^{40} + y^{41}
(x + y)^{42} = x^{42} + 42 x^{41} y + 861 x^{40} y^{2} + 11480 x^{39} y^{3} + 111930 x^{38} y^{4} + 850668 x^{37} y^{5} + 5245786 x^{36} y^{6} + 26978328 x^{35} y^{7} + 118030185 x^{34} y^{8} + 445891810 x^{33} y^{9} + 1471442973 x^{32} y^{10} + 4280561376 x^{31} y^{11} + 11058116888 x^{30} y^{12} + 25518731280 x^{29} y^{13} + 52860229080 x^{28} y^{14} + 98672427616 x^{27} y^{15} + 166509721602 x^{26} y^{16} + 254661927156 x^{25} y^{17} + 353697121050 x^{24} y^{18} + 446775310800 x^{23} y^{19} + 513791607420 x^{22} y^{20} + 538257874440 x^{21} y^{21} + 513791607420 x^{20} y^{22} + 446775310800 x^{19} y^{23} + 353697121050 x^{18} y^{24} + 254661927156 x^{17} y^{25} + 166509721602 x^{16} y^{26} + 98672427616 x^{15} y^{27} + 52860229080 x^{14} y^{28} + 25518731280 x^{13} y^{29} + 11058116888 x^{12} y^{30} + 4280561376 x^{11} y^{31} + 1471442973 x^{10} y^{32} + 445891810 x^{9} y^{33} + 118030185 x^{8} y^{34} + 26978328 x^{7} y^{35} + 5245786 x^{6} y^{36} + 850668 x^{5} y^{37} + 111930 x^{4} y^{38} + 11480 x^{3} y^{39} + 861 x^{2} y^{40} + 42 x y^{41} + y^{42}
(x + y)^{43} = x^{43} + 43 x^{42} y + 903 x^{41} y^{2} + 12341 x^{40} y^{3} + 123410 x^{39} y^{4} + 962598 x^{38} y^{5} + 6096454 x^{37} y^{6} + 32224114 x^{36} y^{7} + 145008513 x^{35} y^{8} + 563921995 x^{34} y^{9} + 1917334783 x^{33} y^{10} + 5752004349 x^{32} y^{11} + 15338678264 x^{31} y^{12} + 36576848168 x^{30} y^{13} + 78378960360 x^{29} y^{14} + 151532656696 x^{28} y^{15} + 265182149218 x^{27} y^{16} + 421171648758 x^{26} y^{17} + 608359048206 x^{25} y^{18} + 800472431850 x^{24} y^{19} + 960566918220 x^{23} y^{20} + 1052049481860 x^{22} y^{21} + 1052049481860 x^{21} y^{22} + 960566918220 x^{20} y^{23} + 800472431850 x^{19} y^{24} + 608359048206 x^{18} y^{25} + 421171648758 x^{17} y^{26} + 265182149218 x^{16} y^{27} + 151532656696 x^{15} y^{28} + 78378960360 x^{14} y^{29} + 36576848168 x^{13} y^{30} + 15338678264 x^{12} y^{31} + 5752004349 x^{11} y^{32} + 1917334783 x^{10} y^{33} + 563921995 x^{9} y^{34} + 145008513 x^{8} y^{35} + 32224114 x^{7} y^{36} + 6096454 x^{6} y^{37} + 962598 x^{5} y^{38} + 123410 x^{4} y^{39} + 12341 x^{3} y^{40} + 903 x^{2} y^{41} + 43 x y^{42} + y^{43}
(x + y)^{44} = x^{44} + 44 x^{43} y + 946 x^{42} y^{2} + 13244 x^{41} y^{3} + 135751 x^{40} y^{4} + 1086008 x^{39} y^{5} + 7059052 x^{38} y^{6} + 38320568 x^{37} y^{7} + 177232627 x^{36} y^{8} + 708930508 x^{35} y^{9} + 2481256778 x^{34} y^{10} + 7669339132 x^{33} y^{11} + 21090682613 x^{32} y^{12} + 51915526432 x^{31} y^{13} + 114955808528 x^{30} y^{14} + 229911617056 x^{29} y^{15} + 416714805914 x^{28} y^{16} + 686353797976 x^{27} y^{17} + 1029530696964 x^{26} y^{18} + 1408831480056 x^{25} y^{19} + 1761039350070 x^{24} y^{20} + 2012616400080 x^{23} y^{21} + 2104098963720 x^{22} y^{22} + 2012616400080 x^{21} y^{23} + 1761039350070 x^{20} y^{24} + 1408831480056 x^{19} y^{25} + 1029530696964 x^{18} y^{26} + 686353797976 x^{17} y^{27} + 416714805914 x^{16} y^{28} + 229911617056 x^{15} y^{29} + 114955808528 x^{14} y^{30} + 51915526432 x^{13} y^{31} + 21090682613 x^{12} y^{32} + 7669339132 x^{11} y^{33} + 2481256778 x^{10} y^{34} + 708930508 x^{9} y^{35} + 177232627 x^{8} y^{36} + 38320568 x^{7} y^{37} + 7059052 x^{6} y^{38} + 1086008 x^{5} y^{39} + 135751 x^{4} y^{40} + 13244 x^{3} y^{41} + 946 x^{2} y^{42} + 44 x y^{43} + y^{44}
(x + y)^{45} = x^{45} + 45 x^{44} y + 990 x^{43} y^{2} + 14190 x^{42} y^{3} + 148995 x^{41} y^{4} + 1221759 x^{40} y^{5} + 8145060 x^{39} y^{6} + 45379620 x^{38} y^{7} + 215553195 x^{37} y^{8} + 886163135 x^{36} y^{9} + 3190187286 x^{35} y^{10} + 10150595910 x^{34} y^{11} + 28760021745 x^{33} y^{12} + 73006209045 x^{32} y^{13} + 166871334960 x^{31} y^{14} + 344867425584 x^{30} y^{15} + 646626422970 x^{29} y^{16} + 1103068603890 x^{28} y^{17} + 1715884494940 x^{27} y^{18} + 2438362177020 x^{26} y^{19} + 3169870830126 x^{25} y^{20} + 3773655750150 x^{24} y^{21} + 4116715363800 x^{23} y^{22} + 4116715363800 x^{22} y^{23} + 3773655750150 x^{21} y^{24} + 3169870830126 x^{20} y^{25} + 2438362177020 x^{19} y^{26} + 1715884494940 x^{18} y^{27} + 1103068603890 x^{17} y^{28} + 646626422970 x^{16} y^{29} + 344867425584 x^{15} y^{30} + 166871334960 x^{14} y^{31} + 73006209045 x^{13} y^{32} + 28760021745 x^{12} y^{33} + 10150595910 x^{11} y^{34} + 3190187286 x^{10} y^{35} + 886163135 x^{9} y^{36} + 215553195 x^{8} y^{37} + 45379620 x^{7} y^{38} + 8145060 x^{6} y^{39} + 1221759 x^{5} y^{40} + 148995 x^{4} y^{41} + 14190 x^{3} y^{42} + 990 x^{2} y^{43} + 45 x y^{44} + y^{45}
(x + y)^{46} = x^{46} + 46 x^{45} y + 1035 x^{44} y^{2} + 15180 x^{43} y^{3} + 163185 x^{42} y^{4} + 1370754 x^{41} y^{5} + 9366819 x^{40} y^{6} + 53524680 x^{39} y^{7} + 260932815 x^{38} y^{8} + 1101716330 x^{37} y^{9} + 4076350421 x^{36} y^{10} + 13340783196 x^{35} y^{11} + 38910617655 x^{34} y^{12} + 101766230790 x^{33} y^{13} + 239877544005 x^{32} y^{14} + 511738760544 x^{31} y^{15} + 991493848554 x^{30} y^{16} + 1749695026860 x^{29} y^{17} + 2818953098830 x^{28} y^{18} + 4154246671960 x^{27} y^{19} + 5608233007146 x^{26} y^{20} + 6943526580276 x^{25} y^{21} + 7890371113950 x^{24} y^{22} + 8233430727600 x^{23} y^{23} + 7890371113950 x^{22} y^{24} + 6943526580276 x^{21} y^{25} + 5608233007146 x^{20} y^{26} + 4154246671960 x^{19} y^{27} + 2818953098830 x^{18} y^{28} + 1749695026860 x^{17} y^{29} + 991493848554 x^{16} y^{30} + 511738760544 x^{15} y^{31} + 239877544005 x^{14} y^{32} + 101766230790 x^{13} y^{33} + 38910617655 x^{12} y^{34} + 13340783196 x^{11} y^{35} + 4076350421 x^{10} y^{36} + 1101716330 x^{9} y^{37} + 260932815 x^{8} y^{38} + 53524680 x^{7} y^{39} + 9366819 x^{6} y^{40} + 1370754 x^{5} y^{41} + 163185 x^{4} y^{42} + 15180 x^{3} y^{43} + 1035 x^{2} y^{44} + 46 x y^{45} + y^{46}
(x + y)^{47} = x^{47} + 47 x^{46} y + 1081 x^{45} y^{2} + 16215 x^{44} y^{3} + 178365 x^{43} y^{4} + 1533939 x^{42} y^{5} + 10737573 x^{41} y^{6} + 62891499 x^{40} y^{7} + 314457495 x^{39} y^{8} + 1362649145 x^{38} y^{9} + 5178066751 x^{37} y^{10} + 17417133617 x^{36} y^{11} + 52251400851 x^{35} y^{12} + 140676848445 x^{34} y^{13} + 341643774795 x^{33} y^{14} + 751616304549 x^{32} y^{15} + 1503232609098 x^{31} y^{16} + 2741188875414 x^{30} y^{17} + 4568648125690 x^{29} y^{18} + 6973199770790 x^{28} y^{19} + 9762479679106 x^{27} y^{20} + 12551759587422 x^{26} y^{21} + 14833897694226 x^{25} y^{22} + 16123801841550 x^{24} y^{23} + 16123801841550 x^{23} y^{24} + 14833897694226 x^{22} y^{25} + 12551759587422 x^{21} y^{26} + 9762479679106 x^{20} y^{27} + 6973199770790 x^{19} y^{28} + 4568648125690 x^{18} y^{29} + 2741188875414 x^{17} y^{30} + 1503232609098 x^{16} y^{31} + 751616304549 x^{15} y^{32} + 341643774795 x^{14} y^{33} + 140676848445 x^{13} y^{34} + 52251400851 x^{12} y^{35} + 17417133617 x^{11} y^{36} + 5178066751 x^{10} y^{37} + 1362649145 x^{9} y^{38} + 314457495 x^{8} y^{39} + 62891499 x^{7} y^{40} + 10737573 x^{6} y^{41} + 1533939 x^{5} y^{42} + 178365 x^{4} y^{43} + 16215 x^{3} y^{44} + 1081 x^{2} y^{45} + 47 x y^{46} + y^{47}
(x + y)^{48} = x^{48} + 48 x^{47} y + 1128 x^{46} y^{2} + 17296 x^{45} y^{3} + 194580 x^{44} y^{4} + 1712304 x^{43} y^{5} + 12271512 x^{42} y^{6} + 73629072 x^{41} y^{7} + 377348994 x^{40} y^{8} + 1677106640 x^{39} y^{9} + 6540715896 x^{38} y^{10} + 22595200368 x^{37} y^{11} + 69668534468 x^{36} y^{12} + 192928249296 x^{35} y^{13} + 482320623240 x^{34} y^{14} + 1093260079344 x^{33} y^{15} + 2254848913647 x^{32} y^{16} + 4244421484512 x^{31} y^{17} + 7309837001104 x^{30} y^{18} + 11541847896480 x^{29} y^{19} + 16735679449896 x^{28} y^{20} + 22314239266528 x^{27} y^{21} + 27385657281648 x^{26} y^{22} + 30957699535776 x^{25} y^{23} + 32247603683100 x^{24} y^{24} + 30957699535776 x^{23} y^{25} + 27385657281648 x^{22} y^{26} + 22314239266528 x^{21} y^{27} + 16735679449896 x^{20} y^{28} + 11541847896480 x^{19} y^{29} + 7309837001104 x^{18} y^{30} + 4244421484512 x^{17} y^{31} + 2254848913647 x^{16} y^{32} + 1093260079344 x^{15} y^{33} + 482320623240 x^{14} y^{34} + 192928249296 x^{13} y^{35} + 69668534468 x^{12} y^{36} + 22595200368 x^{11} y^{37} + 6540715896 x^{10} y^{38} + 1677106640 x^{9} y^{39} + 377348994 x^{8} y^{40} + 73629072 x^{7} y^{41} + 12271512 x^{6} y^{42} + 1712304 x^{5} y^{43} + 194580 x^{4} y^{44} + 17296 x^{3} y^{45} + 1128 x^{2} y^{46} + 48 x y^{47} + y^{48}
(x + y)^{49} = x^{49} + 49 x^{48} y + 1176 x^{47} y^{2} + 18424 x^{46} y^{3} + 211876 x^{45} y^{4} + 1906884 x^{44} y^{5} + 13983816 x^{43} y^{6} + 85900584 x^{42} y^{7} + 450978066 x^{41} y^{8} + 2054455634 x^{40} y^{9} + 8217822536 x^{39} y^{10} + 29135916264 x^{38} y^{11} + 92263734836 x^{37} y^{12} + 262596783764 x^{36} y^{13} + 675248872536 x^{35} y^{14} + 1575580702584 x^{34} y^{15} + 3348108992991 x^{33} y^{16} + 6499270398159 x^{32} y^{17} + 11554258485616 x^{31} y^{18} + 18851684897584 x^{30} y^{19} + 28277527346376 x^{29} y^{20} + 39049918716424 x^{28} y^{21} + 49699896548176 x^{27} y^{22} + 58343356817424 x^{26} y^{23} + 63205303218876 x^{25} y^{24} + 63205303218876 x^{24} y^{25} + 58343356817424 x^{23} y^{26} + 49699896548176 x^{22} y^{27} + 39049918716424 x^{21} y^{28} + 28277527346376 x^{20} y^{29} + 18851684897584 x^{19} y^{30} + 11554258485616 x^{18} y^{31} + 6499270398159 x^{17} y^{32} + 3348108992991 x^{16} y^{33} + 1575580702584 x^{15} y^{34} + 675248872536 x^{14} y^{35} + 262596783764 x^{13} y^{36} + 92263734836 x^{12} y^{37} + 29135916264 x^{11} y^{38} + 8217822536 x^{10} y^{39} + 2054455634 x^{9} y^{40} + 450978066 x^{8} y^{41} + 85900584 x^{7} y^{42} + 13983816 x^{6} y^{43} + 1906884 x^{5} y^{44} + 211876 x^{4} y^{45} + 18424 x^{3} y^{46} + 1176 x^{2} y^{47} + 49 x y^{48} + y^{49}
(x + y)^{50} = x^{50} + 50 x^{49} y + 1225 x^{48} y^{2} + 19600 x^{47} y^{3} + 230300 x^{46} y^{4} + 2118760 x^{45} y^{5} + 15890700 x^{44} y^{6} + 99884400 x^{43} y^{7} + 536878650 x^{42} y^{8} + 2505433700 x^{41} y^{9} + 10272278170 x^{40} y^{10} + 37353738800 x^{39} y^{11} + 121399651100 x^{38} y^{12} + 354860518600 x^{37} y^{13} + 937845656300 x^{36} y^{14} + 2250829575120 x^{35} y^{15} + 4923689695575 x^{34} y^{16} + 9847379391150 x^{33} y^{17} + 18053528883775 x^{32} y^{18} + 30405943383200 x^{31} y^{19} + 47129212243960 x^{30} y^{20} + 67327446062800 x^{29} y^{21} + 88749815264600 x^{28} y^{22} + 108043253365600 x^{27} y^{23} + 121548660036300 x^{26} y^{24} + 126410606437752 x^{25} y^{25} + 121548660036300 x^{24} y^{26} + 108043253365600 x^{23} y^{27} + 88749815264600 x^{22} y^{28} + 67327446062800 x^{21} y^{29} + 47129212243960 x^{20} y^{30} + 30405943383200 x^{19} y^{31} + 18053528883775 x^{18} y^{32} + 9847379391150 x^{17} y^{33} + 4923689695575 x^{16} y^{34} + 2250829575120 x^{15} y^{35} + 937845656300 x^{14} y^{36} + 354860518600 x^{13} y^{37} + 121399651100 x^{12} y^{38} + 37353738800 x^{11} y^{39} + 10272278170 x^{10} y^{40} + 2505433700 x^{9} y^{41} + 536878650 x^{8} y^{42} + 99884400 x^{7} y^{43} + 15890700 x^{6} y^{44} + 2118760 x^{5} y^{45} + 230300 x^{4} y^{46} + 19600 x^{3} y^{47} + 1225 x^{2} y^{48} + 50 x y^{49} + y^{50}