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 A356596 #12 Aug 15 2022 10:30:55
%S A356596 1,1,5,25,162,1231,10988,109481,1220005,14915924,198841997,2861122716,
%T A356596 44290863499,731732469209,12865489418525,239613961313353,
%U A356596 4712991199268122,97557259778360215,2120682504988009054,48270952330701285107,1148400573894718809487
%N A356596 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k)^(1/k!) )^exp(x).
%F A356596 a(0) = 1; a(n) = Sum_{k=1..n} A354338(k) * binomial(n-1,k-1) * a(n-k).
%o A356596 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^(1/k!))^exp(x)))
%o A356596 (PARI) a354338(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!))/(n-k)!);
%o A356596 a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354338(j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A356596 Cf. A354338, A356025.
%K A356596 nonn
%O A356596 0,3
%A A356596 _Seiichi Manyama_, Aug 15 2022