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Search: id:A142336
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| A142336 |
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A generalized PolyLog triangular sequence of coefficients: k = (n + 1); b0 = 1; p(x,n,k)=(k - 1)!*(1 - x)^n*PolyLog[ -n, k, x]/(x*Log[1 - x]); t(n,m)=Coefficients(p(b0,n,k)). |
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+0
1
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| -1, 1, -2, -1, 8, -6, 1, -24, 57, -24, -1, 64, -361, 424, -120, 1, -160, 1890, -4720, 3415, -720, -1, 384, -8828, 41642, -59543, 30036, -5040, 1, -896, 38199, -317072, 803383, -757120, 288449, -40320, -1, 2048, -156483, 2177996, -9156523, 14586084, -9908113, 3015440, -362880, 1, -4608, 615288
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are:
{-1, -1, 1, 10, 6, -294, -1350, 14624, 197568, -703800}.
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FORMULA
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k = (n + 1); b0 = 1; p(x,n,k)=(k - 1)!*(1 - x)^n*PolyLog[ -n, k, x]/(x*Log[1 - x]); t(n,m)=Coefficients(p(b0,n,k)).
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EXAMPLE
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{-1},
{1, -2},
{-1, 8, -6},
{1, -24, 57, -24},
{-1, 64, -361, 424, -120},
{1, -160, 1890, -4720, 3415, -720},
{-1, 384, -8828, 41642, -59543, 30036, -5040},
{1, -896, 38199, -317072, 803383, -757120, 288449, -40320},
{-1, 2048, -156483, 2177996, -9156523, 14586084, -9908113, 3015440, -362880},
{1, -4608, 615288, -13863896, 92378100, -234284376, 258773308, -134868288, 34179471, -3628800}
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MATHEMATICA
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Clear[t, n] k = (n + 1); b0 = 1; t[x_, n_, k_] = (k - 1)!*(1 - x)^n*PolyLog[ -n, k, x]/(x*Log[1 - x]); a = Table[CoefficientList[FullSimplify[Expand[t[x, n, k]]], x], {n, 1, 10}]; a /. x -> 1 - Exp[b0]; Flatten[a /. x -> 1 - Exp[b0]]
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CROSSREFS
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Sequence in context: A004732 A011244 A008517 this_sequence A114193 A039683 A108084
Adjacent sequences: A142333 A142334 A142335 this_sequence A142337 A142338 A142339
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KEYWORD
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uned,sign
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 18 2008
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