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 A384521 #12 Jun 01 2025 09:57:23
%S A384521 1,2,18,218,3474,69290,1659330,46359770,1480241970,53171142410,
%T A384521 2122154748450,93168872862650,4462242691496850,231524863130863850,
%U A384521 12936797161953970050,774495903492069700250,49458416187322116299250,3355754824852804221058250,241081466990843266748993250
%N A384521 Expansion of e.g.f. 5/(7 - 2*exp(5*x)).
%H A384521 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polylogarithm">Polylogarithm</a>.
%F A384521 a(n) = (-5)^(n+1)/7 * Li_{-n}(7/2), where Li_{n}(x) is the polylogarithm function.
%F A384521 a(n) = 5^(n+1)/7 * Sum_{k>=0} k^n * (2/7)^k.
%F A384521 a(n) = Sum_{k=0..n} 2^k * 5^(n-k) * k! * Stirling2(n,k).
%F A384521 a(n) = (2/7) * Sum_{k=0..n} 7^k * (-5)^(n-k) * k! * Stirling2(n,k) for n > 0.
%F A384521 a(0) = 1; a(n) = 2 * Sum_{k=1..n} 5^(k-1) * binomial(n,k) * a(n-k).
%F A384521 a(0) = 1; a(n) = 2 * a(n-1) + 7 * Sum_{k=1..n-1} (-5)^(k-1) * binomial(n-1,k) * a(n-k).
%o A384521 (PARI) a(n) = (-5)^(n+1)*polylog(-n, 7/2)/7;
%Y A384521 Cf. A094419, A384514, A384522, A384523, A384524.
%K A384521 nonn
%O A384521 0,2
%A A384521 _Seiichi Manyama_, Jun 01 2025