A213135 Polylogarithm li(-n,-2/7) multiplied by (9^(n+1))/7.

1, -2, -10, 6, 870, 7878, -90810, -3599514, -20802330, 1466193798, 42164160390, -227736774234, -44798359213530, -896477167975482, 32992662466363590, 2308652347666959846, 16747450938362727270, -3885313022633595475962

Offset

0,2

Comments

See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=2,q=7.

Links

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

Formula

See formula in A212846, setting p=2,q=7.

a(n) = Sum_{k=0..n} k! * (-2)^k * 9^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 2022

Example

polylog(-5,-2/7)*9^6/7 = 7878.

Mathematica

f[n_] := PolyLog[-n, -2/7] 9^(n + 1)/7; f[0] = 1; Array[f, 20, 0] (* Robert G. Wilson v, Dec 25 2015 *)

Prog

(PARI) in A212846; run limnpq(nmax, 2, 7)
(PARI) a(n) = sum(k=0, n, k!*(-2)^k*9^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022

Crossrefs

Cf. A212846, A210246, A212847, A213127 to A213134.

Cf. A213136 to A213157.

Sequence in context: A393330 A346498 A376376 * A037187 A248061 A267500

Adjacent sequences: A213132 A213133 A213134 * A213136 A213137 A213138

Keyword

sign

Author

Stanislav Sykora, Jun 06 2012

Status

approved