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 A356409 #12 Aug 05 2022 15:37:08
%S A356409 1,1,5,28,203,1756,17802,205010,2644287,37669096,586855058,9914829508,
%T A356409 180429770402,3516313661706,73029591042943,1609531482261375,
%U A356409 37504691293842367,920966310015565936,23764054962685200642,642681497080268685092,18174504398294667649782
%N A356409 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k!) )^(1/(1-x)).
%F A356409 a(0) = 1; a(n) = Sum_{k=1..n} A356407(k) * binomial(n-1,k-1) * a(n-k).
%o A356409 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-x^k/k!)^(1/(1-x))))
%o A356409 (PARI) a356407(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!^d)));
%o A356409 a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356407(j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A356409 Cf. A005651, A356025, A356407, A356408.
%K A356409 nonn
%O A356409 0,3
%A A356409 _Seiichi Manyama_, Aug 05 2022