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

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

{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}

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: A302337 A098821 A363322 * A084458 A248933 A353416

Adjacent sequences: A142151 A142152 A142153 * A142155 A142156 A142157

Keyword

sign,uned

Author

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

Status

approved