A142336 A generalized PolyLog triangular sequence of coefficients: k = (n + 1); b0 = 1; p(x,n,k)=(k - 1)!*(1 - x)^n*PolyLog[ -n, k, x]/(x*Log[1 - x]); t(n,m)=Coefficients(p(b0,n,k)).

-1, 1, -2, -1, 8, -6, 1, -24, 57, -24, -1, 64, -361, 424, -120, 1, -160, 1890, -4720, 3415, -720, -1, 384, -8828, 41642, -59543, 30036, -5040, 1, -896, 38199, -317072, 803383, -757120, 288449, -40320, -1, 2048, -156483, 2177996, -9156523, 14586084, -9908113, 3015440, -362880, 1, -4608, 615288

Offset

1,3

Comments

Row sums are:

{-1, -1, 1, 10, 6, -294, -1350, 14624, 197568, -703800}.

Links

Table of n, a(n) for n=1..48.

Formula

k = (n + 1); b0 = 1; p(x,n,k)=(k - 1)!*(1 - x)^n*PolyLog[ -n, k, x]/(x*Log[1 - x]); t(n,m)=Coefficients(p(b0,n,k)).

Example

{-1},
{1, -2},
{-1, 8, -6},
{1, -24, 57, -24},
{-1, 64, -361, 424, -120},
{1, -160, 1890, -4720, 3415, -720},
{-1, 384, -8828, 41642, -59543, 30036, -5040},
{1, -896, 38199, -317072, 803383, -757120, 288449, -40320},
{-1, 2048, -156483, 2177996, -9156523, 14586084, -9908113, 3015440, -362880},
{1, -4608, 615288, -13863896, 92378100, -234284376, 258773308, -134868288, 34179471, -3628800}

Mathematica

Clear[t, n] k = (n + 1); b0 = 1; t[x_, n_, k_] = (k - 1)!*(1 - x)^n*PolyLog[ -n, k, x]/(x*Log[1 - x]); a = Table[CoefficientList[FullSimplify[Expand[t[x, n, k]]], x], {n, 1, 10}]; a /. x -> 1 - Exp[b0]; Flatten[a /. x -> 1 - Exp[b0]]

Crossrefs

Sequence in context: A189966 A367177 A008517 * A193735 A114193 A231846

Adjacent sequences: A142333 A142334 A142335 * A142337 A142338 A142339

Keyword

uned,sign

Author

Roger L. Bagula and Gary W. Adamson, Sep 18 2008

Status

approved