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 A354290 #13 May 23 2022 10:05:27
%S A354290 1,2,14,142,1878,30494,585398,12946910,323717622,9020101470,
%T A354290 276940926646,9283709731806,337237965060982,13191050077634654,
%U A354290 552593521885522486,24677110613547498718,1169994350288769049334,58684818937875321715038
%N A354290 Expansion of e.g.f. exp(f(x) - 1) where f(x) = 1/(3 - 2*exp(x)).
%F A354290 a(0) = 1; a(n) = Sum_{k=1..n} A004123(k+1) * binomial(n-1,k-1) * a(n-k).
%F A354290 a(n) = Sum_{k=0..n} 2^k * A000262(k) * Stirling2(n,k).
%F A354290 a(n) ~ exp(1/(6*log(3/2)) - 5/6 + 2*sqrt(n)/sqrt(3*log(3/2)) - n) * (n^(n - 1/4) / (sqrt(2) * 3^(1/4) * log(3/2)^(n + 1/4))). - _Vaclav Kotesovec_, May 23 2022
%o A354290 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(2*(exp(x)-1)/(3-2*exp(x)))))
%o A354290 (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, 2^k*k!*stirling(j, k, 2))*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A354290 Cf. A075729, A354291.
%Y A354290 Cf. A004123, A354286, A354288.
%K A354290 nonn
%O A354290 0,2
%A A354290 _Seiichi Manyama_, May 23 2022