A213132 Polylogarithm li(-n,-1/9) multiplied by (10^(n+1))/9.

1, -1, -8, -46, 64, 7280, 118720, 406160, -35578880, -1156775680, -12796467200, 444964083200, 27457634713600, 594958346547200, -9096689344716800, -1258068242084608000, -45330583283597312000, 24150498582339584000, 95678058298287259648000, 5379182782796767182848000

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=9.

Examples

			polylog(-5, -1/9)*10^6/9 = 7280.
		

Links

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

Crossrefs

Cf. A212846, A210246, A212847, A213127 to A213131

Cf. A213133 to A213157

Programs

Maple

seq(add((-1)^(n-k)*combinat[eulerian1](n,k)*9^k, k=0..n),n=0..17); # Peter Luschny, Apr 21 2013

Mathematica

Table[If[n == 0, 1, PolyLog[-n, -1/9] 10^(n+1)/9], {n, 0, 19}] (* Jean-François Alcover, Jun 27 2019 *)

PARI

/* See A212846; run limnpq(nmax, 1, 9) */

PARI

x='x+O('x^66); Vec(serlaplace( 10/(9+exp(10*x)) )) \\ Joerg Arndt, Apr 21 2013

PARI

a(n) = sum(k=0, n, k!*(-1)^k*10^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022

Formula

See formula in A212846, setting p=1,q=9.

E.g.f.: 10/(9+exp(10*x)). [Joerg Arndt, Apr 21 2013]

a(n) = Sum_{k=0..n} k! * (-1)^k * 10^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 2022