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Search: id:A142075
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| A142075 |
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A PolyLog functional polynomial coefficient triangular sequence: p(x,n)=(1 - 2*x)^(n + 1)*PolyLog[ -n, 2*x]/(2*x). |
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+0
1
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| 1, 1, 2, 1, 8, 4, 1, 22, 44, 8, 1, 52, 264, 208, 16, 1, 114, 1208, 2416, 912, 32, 1, 240, 4764, 19328, 19056, 3840, 64, 1, 494, 17172, 124952, 249904, 137376, 15808, 128, 1, 1004, 58432, 705872, 2499040, 2823488, 934912, 64256, 256, 1, 2026, 191360
(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, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, 102247563}.
This sequence has logical conjugate substitution :
2x->1-2x;
of the function:
q(x,n)=If[n == 0, 1, (2*x)^(n + 1)*PolyLog[ -n, 1 - 2*x]].
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FORMULA
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p(x,n)=(1 - 2*x)^(n + 1)*PolyLog[ -n, 2*x]/(2*x); t(n,m)=corefficients(p(x,n)).
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EXAMPLE
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{1},
{1, 2},
{1, 8, 4},
{1, 22, 44, 8},
{1, 52, 264, 208, 16},
{1, 114, 1208, 2416, 912, 32},
{1, 240, 4764, 19328, 19056, 3840, 64},
{1, 494, 17172, 124952, 249904, 137376, 15808, 128},
{1, 1004, 58432, 705872, 2499040, 2823488, 934912, 64256, 256},
{1, 2026, 191360, 3641536, 20965664, 41931328, 29132288, 6123520, 259328, 512}
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MATHEMATICA
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Clear[p, x, n, m] p[x_, n_] = (1 - 2*x)^(n + 1)*PolyLog[ -n, 2*x]/(2*x); Table[CoefficientList[p[x, n], x], {n, 1, 10}]; Flatten[%]
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CROSSREFS
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Cf. A008292, A123125.
Sequence in context: A085470 A099379 A133214 this_sequence A110107 A110446 A109979
Adjacent sequences: A142072 A142073 A142074 this_sequence A142076 A142077 A142078
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 15 2008
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