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Search: id:A142249
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| A142249 |
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A triangle of coefficients based on the Nielsen generalized Polylog: p(x,n,k)=(k - 1)!*(1 - x)^(n)*PolyLog[ -n, k, x]/(x*Log[1 - x]); k=2;x=1-Exp[1]; t(n,m)=Coefficients(p(x,n,k). |
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+0
1
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| -1, -1, 1, -1, 2, -1, 3, 3, -1, 4, 19, 4, -1, 5, 80, 65, 5, -1, 6, 286, 566, 181, 6, -1, 7, 945, 3710, 2905, 455, 7, -1, 8, 2997, 20756, 31781, 12636, 1079, 8, -1, 9, 9294, 105299, 278304, 218559, 49754, 2469, 9
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are:
{-1, 0, 1, 5, 26, 154, 1044, 8028, 69264, 663696}.
k=1 in this function gives the Eulerian numbers.
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REFERENCES
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Weisstein, Eric W. "Nielsen Generalized Polylogarithm." http://mathworld.wolfram.com/NielsenGeneralizedPolylogarithm.html
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FORMULA
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p(x,n,k)=(k - 1)!*(1 - x)^(n)*PolyLog[ -n, k, x]/(x*Log[1 - x]); k=2;x=1-Exp[1]; t(n,m)=Coefficients(p(x,n,k).
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EXAMPLE
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{-1},
{-1, 1},
{-1, 2},
{-1, 3, 3},
{-1, 4, 19, 4},
{-1, 5, 80, 65, 5},
{-1, 6, 286, 566, 181, 6},
{-1, 7, 945, 3710, 2905, 455, 7},
{-1, 8, 2997, 20756, 31781, 12636, 1079, 8},
{-1, 9, 9294, 105299, 278304, 218559, 49754, 2469, 9}
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MATHEMATICA
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Clear[t, n] k = 2; t[x_, n_, k_] = (k - 1)!*(1 - x)^(n)*PolyLog[ -n, k, x]/(x*Log[1 - x]); Solve[Log[1 - x] == 1, x]; a = Table[CoefficientList[FullSimplify[Expand[t[x, n, k]]], x], {n, 1, 10}]; a /. x -> 1 - Exp[1]; Flatten[a /. x -> 1 - Exp[1]]
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CROSSREFS
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Cf. A008292.
Sequence in context: A055129 A133804 A089944 this_sequence A097351 A048600 A100578
Adjacent sequences: A142246 A142247 A142248 this_sequence A142250 A142251 A142252
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KEYWORD
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sign,uned,tabl
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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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