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A156365
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Coefficients of infinite sum polynomials: p(x,n)=(1 - 2*x)^(n + 1)*Sum[2^k*(k + 1)^n*x^k, {k, 0, Infinity}].
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0
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1, 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; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Row sums are:
{1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, 102247563,...}.
Apparently another version of A142075, irregular at the top of the triangle. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 19 2009]
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FORMULA
| p(x,n)=(1 - 2*x)^(n + 1)*Sum[2^k*(k + 1)^n*x^k, {k, 0, Infinity}];
p(x,n)=(1 - 2 x)^(1 + n)* PolyLog[ -n, 2 x]/(2*x);
t(n,m)=coefficients(p(x,n)).
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EXAMPLE
| {1},
{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
| Clear[p, x, n, m];
p[x_, n_] = (1 - 2*x)^(n + 1)*Sum[2^k*(k + 1)^n*x^k, {k, 0, Infinity}];
Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A133214 A191935 A142075 * A110107 A154537 A110446
Adjacent sequences: A156362 A156363 A156364 * A156366 A156367 A156368
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 08 2009
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