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Polylogarithm li(-n,-2/5) multiplied by (7^(n+1))/5.
3

%I #22 Nov 20 2024 15:54:29

%S 1,-2,-6,22,426,598,-54006,-568778,8381226,277762198,-123822006,

%T -141432141578,-1958226061974,70457642899798,2812274227385994,

%U -17169209695778378,-3417280244608089174,-48220222006064346602

%N Polylogarithm li(-n,-2/5) multiplied by (7^(n+1))/5.

%C See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=2,q=5.

%H Seiichi Manyama, <a href="/A213134/b213134.txt">Table of n, a(n) for n = 0..399</a> (terms 0..100 from Stanislav Sykora)

%F See formula in A212846, setting p=2,q=5.

%F a(n) = Sum_{k=0..n} k! * (-2)^k * 7^(n-k) * Stirling2(n,k). - _Seiichi Manyama_, Mar 13 2022

%e polylog(-5,-2/5)*7^6/5 = 598.

%t f[n_] := PolyLog[-n, -2/5] 7^(n + 1)/5; f[0] = 1; Array[f, 20, 0] (* _Robert G. Wilson v_, Dec 25 2015 *)

%o (PARI) \\ in A212846; run limnpq(nmax, 2, 5)

%o (PARI) a(n) = sum(k=0, n, k!*(-2)^k*7^(n-k)*stirling(n, k, 2)); \\ _Seiichi Manyama_, Mar 13 2022

%Y Cf. A212846, A210246, A212847, A213127 to A213133.

%Y Cf. A213135 to A213157.

%K sign

%O 0,2

%A _Stanislav Sykora_, Jun 06 2012