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A155871
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Subtraction of polynomial coefficients of MacMahon A060187 from third derivative of Pascal's triangle A155863: p(x,n)=(If[n == 0, 1, x^n + 1 + x*D[( x + 1)^(n + 1), {x, 3}]] - 2^n*(1 - x)^(1 + n)*LerchPhi[x, -n, 1/2])/x.
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0
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1, 1, -16, -110, -16, -117, -1322, -1322, -117, -512, -9703, -22288, -9703, -512, -1843, -58977, -256363, -256363, -58977, -1843, -6048, -328588, -2477728, -4664934, -2477728, -328588, -6048, -18953, -1751300, -21692852, -69388094
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 3,3
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COMMENTS
| Row sums are:
{2, -142, -2878, -42718, -634366, -10289662, -185702398, -3715637758,
-81748930558, -1961988796414, -51011749920766}
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FORMULA
| p(x,n)=(If[n == 0, 1, x^n + 1 + x*D[( x + 1)^(n + 1), {x, 3}]]
- 2^n*(1 - x)^(1 + n)*LerchPhi[x, -n, 1/2])/x;
t(n,m)=coefficients(p(x,n))
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EXAMPLE
| {1, 1},
{-16, -110, -16},
{-117, -1322, -1322, -117},
{-512, -9703, -22288, -9703, -512},
{-1843, -58977, -256363, -256363, -58977, -1843},
{-6048, -328588, -2477728, -4664934, -2477728, -328588, -6048},
{-18953, -1751300, -21692852, -69388094, -69388094, -21692852, -1751300, -18953},
{-58048, -9108221, -178273184, -906867842, -1527023168, -906867842, -178273184, -9108221, -58048},
{-175815, -46690547, -1403033205, -10836712218, -28587853494, -28587853494, -10836712218, -1403033205, -46690547, -175815},
{-529712, -237214810, -10708833968, -121383574287, -477020204064, -743288082732, -477020204064, -121383574287, -10708833968, -237214810, -529712},
{-1592125, -1198358670, -79944129566, -1295922974075, -7310749751463, -16818058154484, -16818058154484, -7310749751463, -1295922974075, -79944129566, -1198358670, -1592125}
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MATHEMATICA
| p[x_, n_] = (If[n == 0, 1, x^n + 1 + x*D[(x + 1)^(n + 1), {x, 3}]] - 2^n*(1 - x)^(1 + n)*LerchPhi[x, -n, 1/2])/x;
Table[FullSimplify[ExpandAll[p[x, n]]], {n, 3, 13}];
a = Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 3, 13}];
Flatten[a]
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CROSSREFS
| A060187, A155863
Sequence in context: A056001 A163725 A165558 * A120668 A053526 A107908
Adjacent sequences: A155868 A155869 A155870 * A155872 A155873 A155874
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 29 2009
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