A213131 Polylogarithm li(-n,-1/8) multiplied by (9^(n+1))/8.

1, -1, -7, -33, 105, 5199, 64953, -46593, -21769335, -497664081, -1941272487, 256114020447, 9566995408425, 99966666676239, -6245895772363527, -366865939437422913, -6924777575908002615, 259022993102904450159, 24387711970312991335833, 716398360186298080983327

Offset: 0

Author

Stanislav Sykora, Jun 06 2012

Keywords

• sign

Comments

See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=1,q=8.

Examples

			polylog(-5,-1/8)*9^6/8 = 5199.
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..100
• OEIS-Wiki, Eulerian polynomials

Crossrefs

Cf. A212846, A210246, A212847, A213127 to A213130

Cf. A213132 to A213157

Programs

Maple

seq(add((-1)^(n-k)*combinat[eulerian1](n,k)*8^k, k=0..n),n=0..17); # Peter Luschny, Apr 21 2013

Mathematica

Table[If[n == 0, 1, PolyLog[-n, -1/8] 9^(n+1)/8], {n, 0, 19}] (* Jean-François Alcover, Jun 27 2019 *)

PARI

/* See A212846; run limnpq(nmax, 1, 8) */

PARI

x='x+O('x^66); Vec(serlaplace( 9/(8+exp(9*x)) )) \\ Joerg Arndt, Apr 21 2013

PARI

a(n) = sum(k=0, n, k!*(-1)^k*9^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022

Formula

See formula in A212846, setting p=1,q=8.

E.g.f.: 9/(8+exp(9*x)). [Joerg Arndt, Apr 21 2013]

a(n) = Sum_{k=0..n} k! * (-1)^k * 9^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 2022