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 A356599 #11 Aug 15 2022 10:30:52
%S A356599 1,1,5,25,159,1201,10488,102901,1121375,13406353,174284898,2445111373,
%T A356599 36799134584,591042564425,10086822013726,182218681622851,
%U A356599 3472980343846199,69632877583186121,1464890891351327598,32260213678562913097,742152913359395190170
%N A356599 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k!) )^exp(x).
%F A356599 a(0) = 1; a(n) = Sum_{k=1..n} A354341(k) * binomial(n-1,k-1) * a(n-k).
%o A356599 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-x^k/k!)^exp(x)))
%o A356599 (PARI) a354341(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!^d))/(n-k)!);
%o A356599 a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354341(j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A356599 Cf. A354341, A356409.
%K A356599 nonn
%O A356599 0,3
%A A356599 _Seiichi Manyama_, Aug 15 2022