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A213133
Polylogarithm li(-n,-1/10) multiplied by (11^(n+1))/10.
4
1, -1, -9, -61, -9, 9659, 197631, 1388099, -51302169, -2339721781, -41290278129, 536297904659, 64956862241271, 2152254297009179, 6320179650231711, -3288155212484644381, -187761119883430045689
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=10.
LINKS
FORMULA
See formula in A212846, setting p=1,q=10.
a(n) = Sum_{k=0..n} k! * (-1)^k * 11^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 2022
EXAMPLE
polylog(-5,-1/10)*11^6/10 = 9659.
MATHEMATICA
f[n_] := PolyLog[-n, -1/10] 11^(n + 1)/10; f[0] = 1; Array[f, 20, 0] (* Robert G. Wilson v, Dec 25 2015 *)
PROG
(PARI) in A212846; run limnpq(nmax, 1, 10)
(PARI) a(n) = sum(k=0, n, k!*(-1)^k*11^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022
CROSSREFS
KEYWORD
sign
AUTHOR
Stanislav Sykora, Jun 06 2012
STATUS
approved