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 A384525 #12 Jun 01 2025 09:57:40
%S A384525 1,1,7,61,679,9445,158095,3088765,68958295,1731875605,48328686175,
%T A384525 1483501074925,49677478279975,1802159471217925,70406303657894575,
%U A384525 2947087948180076125,131584088098220272375,6242270620707298139125,313548981075158413477375
%N A384525 Expansion of e.g.f. 5/(6 - exp(5*x)).
%H A384525 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polylogarithm">Polylogarithm</a>.
%F A384525 a(n) = (-5)^(n+1)/6 * Li_{-n}(6), where Li_{n}(x) is the polylogarithm function.
%F A384525 a(n) = 5^(n+1) * Sum_{k>=0} k^n * (1/6)^(k+1).
%F A384525 a(n) = Sum_{k=0..n} 5^(n-k) * k! * Stirling2(n,k).
%F A384525 a(n) = (1/6) * Sum_{k=0..n} 6^k * (-5)^(n-k) * k! * Stirling2(n,k) for n > 0.
%F A384525 a(0) = 1; a(n) = Sum_{k=1..n} 5^(k-1) * binomial(n,k) * a(n-k).
%F A384525 a(0) = 1; a(n) = a(n-1) + 6 * Sum_{k=1..n-1} (-5)^(k-1) * binomial(n-1,k) * a(n-k).
%o A384525 (PARI) a(n) = (-5)^(n+1)*polylog(-n, 6)/6;
%Y A384525 Cf. A326323.
%K A384525 nonn
%O A384525 0,3
%A A384525 _Seiichi Manyama_, Jun 01 2025