A293298 - OEIS

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A293298

Triangle read by rows, a generalization of the Eulerian numbers based on Nielsen's generalized polylogarithm (case m = 3).

1, 0, 1, 0, 1, -2, 0, 1, -5, 2, 0, 1, -10, 5, 0, 1, -19, 1, 11, 0, 1, -36, -46, 84, 19, 0, 1, -69, -272, 358, 393, 29, 0, 1, -134, -1149, 916, 4171, 1322, 41, 0, 1, -263, -4237, -191, 31939, 26255, 3841, 55, 0, 1, -520, -14536, -20192, 200252, 348848, 130924, 10280, 71

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OFFSET

0,6

COMMENTS

Based on A142249 by Roger L. Bagula and Gary W. Adamson.

LINKS

Table of n, a(n) for n=0..58.

Eric Weisstein's World of Mathematics, Nielsen Generalized Polylogarithm.

FORMULA

Let p(n, m) = (m - 1)!*(1 - x)^n*PolyLog(-n, m, x) and P(n) the polynomial given by the expansion of p(n, m=3) after replacing log(1 - x) by 1. T(n, k) is the k-th coefficient of P(n).

EXAMPLE

Triangle starts:

{1}

{0, 1}

{0, 1, -2}

{0, 1, -5, 2}

{0, 1, -10, 5}

{0, 1, -19, 1, 11}

{0, 1, -36, -46, 84, 19}

{0, 1, -69, -272, 358, 393, 29}

{0, 1, -134, -1149, 916, 4171, 1322, 41}

{0, 1, -263, -4237, -191, 31939, 26255, 3841, 55}

MATHEMATICA

npl[n_, m_] := (m-1)! (1 - x)^n PolyLog[-n, m, x];

A293298Row[0] := {1};

A293298Row[n_] := CoefficientList[FunctionExpand[npl[n, 3]], x] /. Log[1-x] -> 1;

Table[A293298Row[n], {n, 0, 10}] // Flatten

CROSSREFS

A123125 (m=1), A142249 (m=2 with missing first column), this seq. (m=3).

Sequence in context: A351645 A182931 A260615 * A079134 A175528 A163940

Adjacent sequences: A293295 A293296 A293297 * A293299 A293300 A293301

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Oct 11 2017

STATUS

approved