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A142154

A triangular sequence of coefficients of a PolyLog functional polynomials: p(x,n) = 16*x^(n + 1)*PolyLog(-n, (1 - x)/(1 + x))/((1 + x)*(1 - x)).

4, 4, 6, 0, -2, 12, 0, -8, 30, 0, -30, 0, 4, 90, 0, -120, 0, 34, 315, 0, -525, 0, 231, 0, -17, 1260, 0, -2520, 0, 1512, 0, -248, 5670, 0, -13230, 0, 10080, 0, -2640, 0, 124, 28350, 0, -75600, 0, 69930, 0, -25440, 0, 2764

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OFFSET

1,1

COMMENTS

Row sums are all 4.

LINKS

Table of n, a(n) for n=1..50.

FORMULA

p(x,n) = 16*x^(n + 1)*PolyLog(-n, (1 - x)/(1 + x))/((1 + x)*(1 - x)); t(n,m) = coefficients(p(x,n)).

EXAMPLE

Triangle begins:

{4},

{6, 0, -2},

{12, 0, -8},

{30, 0, -30, 0, 4},

{90, 0, -120, 0, 34},

{315, 0, -525, 0, 231, 0, -17},

{1260, 0, -2520, 0, 1512, 0, -248},

{5670, 0, -13230, 0, 10080, 0, -2640, 0, 124},

{28350, 0, -75600, 0, 69930, 0, -25440, 0, 2764}

MATHEMATICA

Clear[w, p]; p[x_, n_] = 16*x^(n + 1)*PolyLog[ -n, (1 - x)/(1 + x)]/((1 + x)*(1 - x)); Table[FullSimplify[ExpandAll[p[x, n]]], {n, 1, 10}]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 1, 10}]; Flatten[%]

CROSSREFS

Sequence in context: A098821 A363322 A374754 * A084458 A248933 A353416

Adjacent sequences: A142151 A142152 A142153 * A142155 A142156 A142157

KEYWORD

sign,uned,tabf

AUTHOR

Roger L. Bagula and Gary W. Adamson, Sep 15 2008

STATUS

approved

URL: https://oeis.org/A142154

⇱ A142154 - OEIS