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A356439 Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k)^(1/k) )^(1/(1-x)).

%I A356439 #8 Aug 07 2022 12:59:15
%S A356439 1,1,6,39,344,3410,42234,567126,8812880,149409144,2793232440,
%T A356439 56224856160,1234342760232,28773852409848,718719835537872,
%U A356439 19045601930731320,534564416062012800,15792205306586537280,491639547448322794944,16024048206145815040704
%N A356439 Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k)^(1/k) )^(1/(1-x)).
%F A356439 a(0) = 1; a(n) = Sum_{k=1..n} A356436(k) * binomial(n-1,k-1) * a(n-k).
%o A356439 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k*x^k)^(1/k))^(1/(1-x))))
%o A356439 (PARI) a356436(n) = n!*sum(k=1, n, sumdiv(k, d, d^(k/d))/k);
%o A356439 a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356436(j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A356439 Cf. A353993, A356436, A356440.
%K A356439 nonn
%O A356439 0,3
%A A356439 _Seiichi Manyama_, Aug 07 2022