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 A365558 #18 Nov 16 2023 11:50:11
%S A365558 1,2,12,112,1432,23272,458952,10644552,283851272,8555351112,
%T A365558 287585280392,10666369505992,432674936431112,19054822031194952,
%U A365558 905387807689821832,46166008179076287432,2514469578906179506952,145691888630159515550792
%N A365558 Expansion of e.g.f. 1 / (4 - 3 * exp(x))^(2/3).
%F A365558 a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (3*j+2)) * Stirling2(n,k).
%F A365558 a(0) = 1; a(n) = Sum_{k=1..n} (3 - k/n) * binomial(n,k) * a(n-k).
%F A365558 a(n) ~ sqrt(3) * Gamma(1/3) * n^(n + 1/6) / (sqrt(Pi) * 2^(11/6) * exp(n) * log(4/3)^(n + 2/3)). - _Vaclav Kotesovec_, Nov 11 2023
%F A365558 a(0) = 1; a(n) = 2*a(n-1) - 4*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k). - _Seiichi Manyama_, Nov 16 2023
%t A365558 a[n_] := Sum[Product[3*j + 2, {j, 0, k - 1}] * StirlingS2[n, k], {k, 0, n}]; Array[a, 18, 0] (* _Amiram Eldar_, Sep 11 2023 *)
%o A365558 (PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 3*j+2)*stirling(n, k, 2));
%Y A365558 Cf. A032033, A346982.
%K A365558 nonn
%O A365558 0,2
%A A365558 _Seiichi Manyama_, Sep 09 2023