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 A365575 #14 Nov 11 2023 05:35:52
%S A365575 1,2,12,114,1482,24468,490020,11538840,312363720,9556741440,
%T A365575 326076452640,12275391192480,505400508041760,22590511357965120,
%U A365575 1089423938332883520,56379459359942190720,3116574045158647605120,183271869976364873222400
%N A365575 Expansion of e.g.f. 1 / (1 + 3 * log(1-x))^(2/3).
%F A365575 a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (3*j+2)) * |Stirling1(n,k)|.
%F A365575 a(0) = 1; a(n) = Sum_{k=1..n} (3 - k/n) * (k-1)! * binomial(n,k) * a(n-k).
%F A365575 a(n) ~ Gamma(1/3) * n^(n + 1/6) / (3^(1/6) * sqrt(2*Pi) * (exp(1/3) - 1)^(n + 2/3) * exp(2*n/3)). - _Vaclav Kotesovec_, Nov 11 2023
%t A365575 a[n_] := Sum[Product[3*j + 2, {j, 0, k - 1}] * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 18, 0] (* _Amiram Eldar_, Sep 11 2023 *)
%o A365575 (PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 3*j+2)*abs(stirling(n, k, 1)));
%Y A365575 Cf. A347015, A354263.
%K A365575 nonn
%O A365575 0,2
%A A365575 _Seiichi Manyama_, Sep 09 2023