A213130 Polylogarithm li(-n,-1/7) multiplied by (8^(n+1))/7.

1, -1, -6, -22, 120, 3464, 30864, -189232, -11564160, -173474176, 923222784, 112587838208, 2509094415360, -7947533372416, -2393798607108096, -74042111038461952, -8461127118520320, 94056121376877215744

Offset

0,3

Comments

See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=1,q=7.

Links

Stanislav Sykora, Table of n, a(n) for n = 0..100

OEIS-Wiki, Eulerian polynomials

Formula

See formula in A212846, setting p=1,q=7.

a(n) = Sum_{k=0..n} k! * (-1)^k * 8^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 2022

Example

polylog(-5,-1/7)*8^6/7 = 3464.

Maple

seq(add((-1)^(n-k)*combinat[eulerian1](n, k)*7^k, k=0..n), n=0..17); # Peter Luschny, Apr 21 2013

Mathematica

f[n_] := PolyLog[-n, -1/7] 8^(n + 1)/7; f[0] = 1; Array[f, 20, 0] (* Robert G. Wilson v, Dec 25 2015 *)

Prog

(PARI) in A212846; run limnpq(nmax, 1, 7)
(PARI) a(n) = sum(k=0, n, k!*(-1)^k*8^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022

Crossrefs

Cf. A212846, A210246, A212847, A213127 to A213129.

Cf. A213131 through A213157.

Sequence in context: A193463 A319214 A009358 * A002137 A009361 A193445

Adjacent sequences: A213127 A213128 A213129 * A213131 A213132 A213133

Keyword

sign

Author

Stanislav Sykora, Jun 06 2012

Status

approved