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%I #12 Aug 09 2022 11:20:01
%S 1,1,6,45,580,7105,170076,2654575,116426528,2386183761,209503380160,
%T 3455683548691,969334978024920,15164681616944353,6510178188269825720,
%U 223847763757748796975,81261936394687862700256,1581790511799886415713825
%N Expansion of e.g.f. Product_{k>0} 1/(1 - (k * x)^k)^(1/k!).
%F a(0) = 1; a(n) = Sum_{k=1..n} A356486(k) * binomial(n-1,k-1) * a(n-k).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(k*x)^k)^(1/k!))))
%o (PARI) a356486(n) = (n-1)!*sumdiv(n, d, d^n/(d-1)!);
%o a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356486(j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y Cf. A023882, A209902, A356486.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 09 2022
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