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%I #10 Aug 14 2022 10:15:50
%S 1,0,2,9,44,450,2754,45360,340304,6481944,81801000,1370631240,
%T 21731534472,511117017840,8113055559504,193958323289640,
%U 4765385232157440,108183734293844160,2754467397591689664,80416694712647352960,2132862160676063137920,67803682111729108433280
%N Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k)^(1/k) )^x.
%F a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k! * A055225(k-1)/(k-1) * binomial(n-1,k-1) * a(n-k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k*x^k)^(1/k))^x))
%o (PARI) a055225(n) = sumdiv(n, d, d^(n/d));
%o a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j!*a055225(j-1)/(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y Cf. A055225, A355064, A356439, A356587.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 14 2022