%I #58 Aug 04 2022 11:00:17
%S 1,1,5,28,206,1786,18347,212745,2773927,39901109,628298992,
%T 10725440221,197349522471,3888090474399,81659016005387,
%U 1820049574958950,42895622543757084,1065460090285463634,27811791343693345811,760920657403831436463
%N Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k)^(1/k!) )^(1/(1-x)).
%F a(0) = 1; a(n) = Sum_{k=1..n} A356009(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-x^k)^(1/k!)))^(1/(1-x))))
%o (PARI) a356009(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!)));
%o a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356009(j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y Cf. A209902, A356009, A356336.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 04 2022
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