计算 n 阶行列式的值

王守恩

接2楼。学习了。 谢谢天山草！
\(D_{0}=1,\)
\(D_{1}=2 \cos(A),\)
\(D_{2}=4\cos^2(A)-1,\)
\(D_{3}=8\cos^3(A)-4\cos(A),\)
\(D_{4}=16\cos^4(A)-12\cos^2(A)+1,\)
\(D_{5}=32\cos^5(A)-32\cos^3(A)+6\cos(A),\)
\(D_{6}=64\cos^6(A)-80\cos^4(A)+24\cos^2(A)-1,\)
\(D_{7}=128\cos^7(A)-192\cos^5(A)+80\cos^3(A)-8\cos(A),\)
\(D_{8}=256\cos^8(A)-448\cos^6(A)+240\cos^4(A)-40\cos^2(A)+1,\)
\(D_{9}=512\cos^9(A)-1024\cos^7(A)+672\cos^5(A)-160\cos^3(A)+10\cos(A),\)
......

1. Table[Sum[((n - k)! (2 Cos[A])^(n - 2 k))/(k! (n - 2 k)! (-1)^k), {k, 0, n/2}], {n, 16}]

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第1列。{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768},
第2列。{1, 4, 12, 32, 80, 192, 448, 1024, 2304, 5120, 11264, 24576, 53248, 114688, 245760, 524288},
第3列。{1, 6, 24, 80, 240, 672, 1792, 4608, 11520, 28160, 67584, 159744, 372736, 860160, 1966080, 4456448},
第4列。{1, 8, 40, 160, 560, 1792, 5376, 15360, 42240, 112640, 292864, 745472, 1863680, 4587520, 11141120, 26738688},
第5列。{1, 10, 60, 280, 1120, 4032, 13440, 42240, 126720, 366080, 1025024, 2795520, 7454720, 19496960, 50135040, 127008768},
第6列。{1, 12, 84, 448, 2016, 8064, 29568, 101376, 329472, 1025024, 3075072, 8945664, 25346048, 70189056, 190513152, 508035072},
第7列。{1, 14, 112, 672, 3360, 14784, 59136, 219648, 768768, 2562560, 8200192, 25346048, 76038144, 222265344, 635043840, 1778122752},
第8列。{1, 16, 144, 960, 5280, 25344, 109824, 439296, 1647360, 5857280, 19914752, 65175552, 206389248, 635043840, 1905131520, 5588385792},
第9列。{1, 18, 180, 1320, 7920, 41184, 192192, 823680, 3294720, 12446720, 44808192, 154791936, 515973120, 1666990080, 5239111680, 16066609152},
......

1. Table[(n! 2^(n - k))/(k! (n - k)!), {k, 0, 9}, {n, k, 15 + k}]

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