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A143197
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Triangle read by rows: imaginary part of polylog expansion of Eulerian numbers: p(x,n)=(1 - I*x)^(n + 1)*PolyLog[ -n, I*x]/x.
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0
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1, 1, 0, 1, 0, -1, 1, 0, -23, 0, 1, 0, -230, 0, 1, 1, 0, -1682, 0, 237, 0, 1, 0, -10543, 0, 10543, 0, -1, 1, 0, -60657, 0, 259723, 0, -2179, 0, 1, 0, -331612, 0, 4675014, 0, -331612, 0, 1, 1, 0, -1756340, 0, 69413294, 0, -21707972, 0, 19673, 0, 1, 0, -9116141, 0, 906923282, 0, -906923282, 0, 9116141, 0, -1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,9
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COMMENTS
| Row sums are: {1, 1, 1, 0, -10, -64, -244, 0, 11080, 126976, 808336, ...}.
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FORMULA
| p(x,n)=(1 - I*x)^(n + 1)*PolyLog[ -n, I*x]/x; t(n,m)=ImaginaryCoefficients(p(x,n)).
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EXAMPLE
| {1},
{1},
{1, 0},
{1, 0, -1},
{1, 0, -11, 0},
{1, 0, -66, 0, 1},
{1, 0, -302, 0, 57, 0},
{1, 0, -1191, 0, 1191, 0, -1},
{1, 0, -4293, 0, 15619, 0, -247, 0},
{1, 0, -14608, 0, 156190, 0, -14608, 0, 1},
{1, 0, -47840, 0, 1310354, 0, -455192, 0, 1013, 0}
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MATHEMATICA
| Clear[p, x, n, a]; p[x_, n_] = p[x_, n_] = (1 - I*x)^(n + 1)*PolyLog[ -n, I*x]/x; Table[FullSimplify[Expand[p[x, n]]], {n, 0, 10}]; Table[Im[CoefficientList[FullSimplify[Expand[p[x, n]]], x]], {n, 0, 10}]; Flatten[%]
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CROSSREFS
| Cf. A060187.
Sequence in context: A180729 A119566 A143196 * A092993 A114784 A141517
Adjacent sequences: A143194 A143195 A143196 * A143198 A143199 A143200
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KEYWORD
| tabf,uned,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 19 2008
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EXTENSIONS
| The entries here are clearly all wrong (compare the example lines). What are the real parts? - N. J. A. Sloane (njas(AT)research.att.com), Oct 25 2008
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