%I #29 Aug 06 2022 10:14:22
%S 1,1,8,63,668,7850,115914,1847286,34031024,682177464,15049816200,
%T 357564279600,9212847784392,252552128708568,7395084613746816,
%U 229412209982127480,7524339637608261120,259675490280634374720,9418707076419411194304,357606237255136232451264
%N Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k) )^(1/(1-x)).
%F a(0) = 1; a(n) = Sum_{k=1..n} A353992(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/(1-x))))
%o (PARI) a353992(n) = n!*sum(k=1, n, sumdiv(k, d, (k/d)^d/d));
%o a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a353992(j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y Cf. A006906, A353992, A356335, A356337, A356408.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 06 2022