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 A212847 #24 Sep 03 2024 15:03:01 %S A212847 1,-2,-2,22,94,-890,-9170,67030,1495870,-6581210,-362016050,194447350, %T A212847 120002960350,554823694150,-51277487618450,-601106981110250, %U A212847 26775789844186750,591304973974171750,-16113120605399179250 %N A212847 Polylogarithm li(-n,-2/3) multiplied by (5^(n+1))/3. %C A212847 See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=2,q=3. %H A212847 Stanislav Sykora, <a href="/A212847/b212847.txt">Table of n, a(n) for n = 0..100</a> %F A212847 See formula in A212846, setting p=2,q=3. %F A212847 From _Vaclav Kotesovec_, May 17 2022: (Start) %F A212847 E.g.f.: 5/(3 + 2*exp(5*x)). %F A212847 a(n) ~ n! * 2*(log(3/2) * cos(n*arctan(Pi/log(3/2))) - Pi * sin(n*arctan(Pi/log(3/2)))) * 5^(n+1) / (3 * (Pi^2 + log(3/2)^2)^(1 + n/2)). (End) %e A212847 polylog(-5,-2/3)*5^6/3 = -890. %t A212847 f[n_] := PolyLog[-n, -2/3] 5^(n + 1)/3; f[0] = 1; Array[f, 20, 0] (* _Robert G. Wilson v_, Dec 25 2015 *) %o A212847 (PARI) \\ See A212846; run limnpq(nmax,2,3) %Y A212847 Cf. A212846 (li(-n,-1/2)), A210246 (li(-n,-1/3)). %Y A212847 Cf. A213127 through A213157. %K A212847 sign %O A212847 0,2 %A A212847 _Stanislav Sykora_, May 28 2012