This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A213130 #22 Sep 28 2024 14:24:35
%S A213130 1,-1,-6,-22,120,3464,30864,-189232,-11564160,-173474176,923222784,
%T A213130 112587838208,2509094415360,-7947533372416,-2393798607108096,
%U A213130 -74042111038461952,-8461127118520320,94056121376877215744
%N A213130 Polylogarithm li(-n,-1/7) multiplied by (8^(n+1))/7.
%C A213130 See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=1,q=7.
%H A213130 Stanislav Sykora, <a href="/A213130/b213130.txt">Table of n, a(n) for n = 0..100</a>
%H A213130 OEIS-Wiki, <a href="http://oeis.org/wiki/Eulerian_polynomials">Eulerian polynomials</a>
%F A213130 See formula in A212846, setting p=1,q=7.
%F A213130 a(n) = Sum_{k=0..n} k! * (-1)^k * 8^(n-k) * Stirling2(n,k). - _Seiichi Manyama_, Mar 13 2022
%e A213130 polylog(-5,-1/7)*8^6/7 = 3464.
%p A213130 seq(add((-1)^(n-k)*combinat[eulerian1](n,k)*7^k, k=0..n),n=0..17); # _Peter Luschny_, Apr 21 2013
%t A213130 f[n_] := PolyLog[-n, -1/7] 8^(n + 1)/7; f[0] = 1; Array[f, 20, 0] (* _Robert G. Wilson v_, Dec 25 2015 *)
%o A213130 (PARI) \\ in A212846; run limnpq(nmax, 1, 7)
%o A213130 (PARI) a(n) = sum(k=0, n, k!*(-1)^k*8^(n-k)*stirling(n, k, 2)); \\ _Seiichi Manyama_, Mar 13 2022
%Y A213130 Cf. A212846, A210246, A212847, A213127 to A213129.
%Y A213130 Cf. A213131 through A213157.
%K A213130 sign
%O A213130 0,3
%A A213130 _Stanislav Sykora_, Jun 06 2012