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 A356408 #12 Aug 05 2022 15:37:04
%S A356408 1,1,5,29,216,1919,20012,236977,3145832,46122546,739703182,
%T A356408 12865212172,241040899668,4836265824740,103410589256452,
%U A356408 2346358252787094,56285005757022752,1422783492250963296,37790069818311971640,1051924374853915254048
%N A356408 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k) )^(1/(1-x)).
%F A356408 a(0) = 1; a(n) = Sum_{k=1..n} A356406(k) * binomial(n-1,k-1) * a(n-k).
%o A356408 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-x^k/k)^(1/(1-x))))
%o A356408 (PARI) a356406(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)^d)));
%o A356408 a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356406(j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A356408 Cf. A007841, A356336, A356406, A356409.
%K A356408 nonn
%O A356408 0,3
%A A356408 _Seiichi Manyama_, Aug 05 2022