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 A367371 #13 Jun 09 2025 10:45:16
%S A367371 1,2,8,52,468,5372,74948,1230812,23251908,496661532,11834467588,
%T A367371 311195370972,8950935130948,279540192840092,9419760953149828,
%U A367371 340658973061341532,13160048773006619588,540850933969855649052,23561995002376443953668
%N A367371 Expansion of the e.g.f. (exp(x) / (3 - 2*exp(x)))^(2/3).
%F A367371 a(n) = Sum_{k=0..n} (-1)^(n-k) * (Product_{j=0..k-1} (3*j+2)) * Stirling2(n,k).
%F A367371 a(0) = 1; a(n) = Sum_{k=1..n} (-1)^k * (k/n - 3) * binomial(n,k) * a(n-k).
%F A367371 a(0) = 1; a(n) = 2*a(n-1) + 2*Sum_{k=1..n-1} binomial(n-1,k) * a(n-k).
%F A367371 a(n) ~ n! / (2^(2/3) * Gamma(2/3) * n^(1/3) * log(3/2)^(n + 2/3)). - _Vaclav Kotesovec_, Jun 09 2025
%o A367371 (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*prod(j=0, k-1, 3*j+2)*stirling(n, k, 2));
%Y A367371 Cf. A136727, A201339.
%Y A367371 Cf. A365558.
%K A367371 nonn
%O A367371 0,2
%A A367371 _Seiichi Manyama_, Nov 15 2023