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A142073
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A triangular sequence of coefficiencts of and infinite sum polynomial: p(x,n)=(1 - 2*x)^(n + 1)*Sum[k^n*(x/(1 - x))^k, {k, 0, Infinity}]/x; p(x,n)=(1 - 2*x)^(n + 1)*PolyLog[ -n,x/(1-x)]/x;.
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0
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1, 1, -1, 1, -1, 1, 1, -4, 2, 1, 7, -16, 8, 1, 21, -28, -26, 48, -16, 1, 51, 32, -356, 408, -136, 1, 113, 492, -1774, 1072, 912, -1088, 272, 1, 239, 2592, -5008, -6656, 20736, -15872, 3968, 1, 493, 10628, -50, -94432, 154528, -57856, -45056, 39680, -7936, 1, 1003, 38768, 108820, -621352, 455608, 848384
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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COMMENTS
| Except for n=0, the row sums are zero.
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FORMULA
| p(x,n)=(1 - 2*x)^(n + 1)*Sum[k^n*(x/(1 - x))^k, {k, 0, Infinity}]/x; p(x,n)=(1 - 2*x)^(n + 1)*PolyLog[ -n,x/(1-x)]/x; t(n,m)=coefficients(p(x,n)).
p(x,n)=Sum(eulerian(n,k)*(x-1)^(k+1),k=0..n); t(n,m)=Coefficients(p(x,n)). [From Mourad Rahmani (mrahmani(AT)usthb.dz), Aug 29 2010]
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EXAMPLE
| {1},
{1, -1},
{1, -1},
{1, 1, -4, 2},
{1, 7, -16, 8},
{1, 21, -28, -26, 48, -16},
{1, 51, 32, -356, 408, -136},
{1, 113, 492, -1774, 1072, 912, -1088,272},
{1, 239, 2592, -5008, -6656, 20736, -15872, 3968},
{1, 493, 10628, -50, -94432, 154528, -57856, -45056, 39680, -7936},
{1, 1003, 38768, 108820, -621352, 455608, 848384, -1538816, 884480, -176896}
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MATHEMATICA
| p[x_, n_] = (1 - 2*x)^(n + 1)*Sum[k^n*(x/(1 - x))^k, {k, 0, Infinity}]/x; 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
| Cf. A141720.
Cf. A008292 [From Mourad Rahmani (mrahmani(AT)usthb.dz), Aug 29 2010]
Sequence in context: A046741 A136249 A142147 * A193559 A135294 A175938
Adjacent sequences: A142070 A142071 A142072 * A142074 A142075 A142076
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KEYWORD
| sign,uned
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 15 2008
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