A213129 Polylogarithm li(-n,-1/6) multiplied by (7^(n+1))/6.

1, -1, -5, -13, 115, 2099, 11395, -177373, -5116685, -40481581, 948973795, 36701972867, 375364322515, -12090607539661, -580544884927805, -7188739235243293, 301374306966657715, 17150539711123411859, 246564346727945106595, -12988846468460187345853

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=6.

Examples

			polylog(-5,-1/6)*7^6/6 = 2099.
		

Links

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

Crossrefs

Cf. A212846, A210246, A212847, A213127, A213128.

Cf. A213130 through A213157

Programs

Maple

seq(add((-1)^(n-k)*combinat[eulerian1](n,k)*6^k, k=0..n),n=0..17); # Peter Luschny, Apr 21 2013

Mathematica

Table[If[n == 0, 1, PolyLog[-n, -1/6] 7^(n+1)/6], {n, 0, 19}] (* Jean-François Alcover, Jun 27 2019 *)

PARI

/* See A212846; run limnpq(nmax,1,6) */

PARI

x='x+O('x^66); Vec(serlaplace( 7/(6+exp(7*x)) )) \\ Joerg Arndt, Apr 21 2013

PARI

a(n) = sum(k=0, n, k!*(-1)^k*7^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022

Formula

See formula in A212846, setting p=1,q=6.

E.g.f.: 7/(6+exp(7*x)). [Joerg Arndt, Apr 21 2013]

a(n) = Sum_{k=0..n} k! * (-1)^k * 7^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 2022