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A146749
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Coefficients pf the Pascal sequence minus the Eulerian numbers: q(x,n)= = (1 - x)^(n + 1)*PolyLog[ -n, x]; p(x,n) = (q(x, n)/x - (x + 1)^(n - 1))/x.
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0
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2, 8, 8, 22, 60, 22, 52, 292, 292, 52, 114, 1176, 2396, 1176, 114, 240, 4272, 15584, 15584, 4272, 240, 494, 14580, 88178, 156120, 88178, 14580, 494, 1004, 47804, 455108, 1310228, 1310228, 455108, 47804, 1004
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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COMMENTS
| Row sums are:{2, 16, 104, 688, 4976, 40192, 362624, 3628288}. First row elements/column are:A005803;f(n)=2^n - 2n; {2, 8, 22, 52, 114, 240, 494, 1004}.
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FORMULA
| q(x,n)= = (1 - x)^(n + 1)*PolyLog[ -n, x]; p(x,n) = (q(x, n)/x - (x + 1)^(n - 1))/x; t(n,m)=Coefficients(p(x,n)).
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EXAMPLE
| {2}, {8, 8}, {22, 60, 22}, {52, 292, 292, 52}, {114, 1176, 2396, 1176, 114}, {240, 4272, 15584, 15584, 4272, 240}, {494, 14580, 88178, 156120, 88178, 14580, 494}, {1004, 47804, 455108, 1310228, 1310228, 455108, 47804, 1004}
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MATHEMATICA
| q[x_, n_] = (1 - x)^(n + 1)*PolyLog[ -n, x]; p[x_, n_] = (q[x, n]/x - (x + 1)^(n - 1))/x; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 3, 10}]; Flatten[%]
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CROSSREFS
| A005803
Sequence in context: A019240 A093907 A116471 * A180825 A064231 A181130
Adjacent sequences: A146746 A146747 A146748 * A146750 A146751 A146752
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 01 2008
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