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 A354289 #14 May 23 2022 09:46:22
%S A354289 1,3,24,276,4086,73620,1557702,37770138,1030916484,31245154164,
%T A354289 1040274476208,37716394860936,1478413316987424,62274364390387656,
%U A354289 2804282634867538248,134397620584518275928,6828489621874434752208,366547074721109281366128
%N A354289 Expansion of e.g.f. (1 + x)^(3/(1 - 3 * log(1+x))).
%F A354289 a(0) = 1; a(n) = Sum_{k=1..n} A335531(k) * binomial(n-1,k-1) * a(n-k).
%F A354289 a(n) = Sum_{k=0..n} 3^k * A000262(k) * Stirling1(n,k).
%F A354289 a(n) ~ exp(-11/12 + 1/(6*(exp(1/3) - 1)) + 2*exp(1/6)*sqrt(n)/sqrt(3*(exp(1/3) - 1)) - n) * n^(n - 1/4) / (sqrt(2) * 3^(1/4) * (exp(1/3) - 1)^(n + 1/4)). - _Vaclav Kotesovec_, May 23 2022
%o A354289 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)^(3/(1-3*log(1+x)))))
%o A354289 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, sum(k=0, j, 3^k*k!*stirling(j, k, 1))*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A354289 Cf. A088819, A354288.
%Y A354289 Cf. A000262, A335531, A354287, A354291.
%K A354289 nonn
%O A354289 0,2
%A A354289 _Seiichi Manyama_, May 23 2022