シュワルツの定理
「ラマヌジャンの遺した関数」の2.7 に載っている定理を確かめてみる。
a(n, m) = binomial(n^2, n)%n^m;
for(m=1, 6, for(n=1, 50, print1(a(n, m),", ")); print)
出力結果
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 2, 3, 12, 5, 12, 7, 56, 9, 40, 11, 108, 13, 84, 90, 240, 17, 144, 19, 80, 315, 220, 23, 72, 25, 312, 27, 560, 29, 0, 31, 992, 759, 544, 770, 720, 37, 684, 1053, 520, 41, 252, 43, 1408, 1125, 1012, 47, 1872, 49, 1200,
0, 6, 3, 28, 5, 120, 7, 120, 9, 440, 11, 828, 13, 1064, 315, 496, 17, 2088, 19, 2080, 7812, 3608, 23, 648, 25, 5720, 6588, 10752, 29, 1800, 31, 18400, 29073, 12104, 36295, 12384, 37, 16568, 36036, 54920, 41, 12600, 43, 69168, 74025, 28520, 47, 54864, 49, 36200,
0, 6, 3, 28, 5, 1200, 7, 3192, 2925, 6440, 11, 828, 13, 14784, 10440, 12784, 17, 25416, 19, 34080, 118944, 205920, 23, 111240, 156275, 286936, 262467, 515648, 29, 244800, 31, 575456, 640002, 169320, 36295, 712224, 37, 1827344, 2230839, 2166920, 41, 2012976, 43, 1091376, 3445650, 1683232, 47, 54864, 823592, 2036200,
0, 6, 84, 796, 5, 3792, 7, 27768, 22608, 56440, 11, 83772, 13, 168448, 61065, 471536, 17, 445320, 19, 994080, 2258235, 4188272, 23, 6083208, 156275, 743912, 13548492, 3588928, 29, 16444800, 31, 28887008, 13685133, 2841992, 42053795, 49421088, 37, 24763840, 9171162, 45686920, 41, 101587248, 43, 98541872, 15747525, 64367616, 47, 153998928, 58471602, 133286200,
0, 6, 84, 1820, 6255, 34896, 16814, 126072, 258804, 456440, 805266, 2820924, 2227771, 3933216, 1579815, 7811568, 9939016, 26899272, 12380514, 994080, 47183346, 112414544, 32181738, 22008456, 205234400, 131439048, 157037562, 365006656, 184600370, 210844800, 429437296, 699975648, 796392993, 502631656, 1460144420, 2044804896, 901471478, 1767937536, 2264776137, 1888886920, 2780548865, 1016425872, 735042258, 6860107056, 6843288150, 9332701536, 1834760103, 3211646544, 9380154819, 8883286200,
0 件のコメント:
コメントを投稿
注: コメントを投稿できるのは、このブログのメンバーだけです。