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%I #15 Mar 13 2022 11:15:26
%S 1,-1,-9,-61,-9,9659,197631,1388099,-51302169,-2339721781,
%T -41290278129,536297904659,64956862241271,2152254297009179,
%U 6320179650231711,-3288155212484644381,-187761119883430045689
%N Polylogarithm li(-n,-1/10) multiplied by (11^(n+1))/10.
%C See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=1,q=10.
%H Stanislav Sykora, <a href="/A213133/b213133.txt">Table of n, a(n) for n = 0..100</a>
%F See formula in A212846, setting p=1,q=10.
%F a(n) = Sum_{k=0..n} k! * (-1)^k * 11^(n-k) * Stirling2(n,k). - _Seiichi Manyama_, Mar 13 2022
%e polylog(-5,-1/10)*11^6/10 = 9659.
%t f[n_] := PolyLog[-n, -1/10] 11^(n + 1)/10; f[0] = 1; Array[f, 20, 0] (* _Robert G. Wilson v_, Dec 25 2015 *)
%o (PARI) in A212846; run limnpq(nmax, 1, 10)
%o (PARI) a(n) = sum(k=0, n, k!*(-1)^k*11^(n-k)*stirling(n, k, 2)); \\ _Seiichi Manyama_, Mar 13 2022
%Y Cf. A212846, A210246, A212847, A213127 to A213132.
%Y Cf. A213134 to A213157.
%K sign
%O 0,3
%A _Stanislav Sykora_, Jun 06 2012
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