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 A384435 #20 Jun 03 2025 08:43:03
%S A384435 1,3,24,282,4416,86448,2030784,55656912,1743277056,61427981568,
%T A384435 2405046994944,103579443604992,4866448609591296,247692476576575488,
%U A384435 13576823521525653504,797345878311609526272,49948684871884896731136,3324530341927517641310208,234293439367907438337982464
%N A384435 Expansion of e.g.f. 2/(5 - 3*exp(2*x)).
%H A384435 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polylogarithm">Polylogarithm</a>.
%F A384435 a(n) = (-2)^(n+1)/5 * Li_{-n}(5/3), where Li_{n}(x) is the polylogarithm function.
%F A384435 a(n) = 2^(n+1)/5 * Sum_{k>=0} k^n * (3/5)^k.
%F A384435 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * k! * Stirling2(n,k).
%F A384435 a(n) = (3/5) * A201366(n) = (3/5) * Sum_{k=0..n} 5^k * (-2)^(n-k) * k! * Stirling2(n,k) for n > 0.
%F A384435 a(0) = 1; a(n) = 3 * Sum_{k=1..n} 2^(k-1) * binomial(n,k) * a(n-k).
%F A384435 a(0) = 1; a(n) = 3 * a(n-1) + 5 * Sum_{k=1..n-1} (-2)^(k-1) * binomial(n-1,k) * a(n-k).
%o A384435 (PARI) a(n) = (-2)^(n+1)*polylog(-n, 5/3)/5;
%Y A384435 Cf. A094417, A326324, A382753.
%Y A384435 Cf. A032033, A328182, A384522.
%Y A384435 Cf. A201366.
%K A384435 nonn
%O A384435 0,2
%A A384435 _Seiichi Manyama_, Jun 03 2025