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A356595 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k)^k )^exp(x).

%I A356595 #11 Aug 15 2022 08:45:52
%S A356595 1,1,8,60,582,6555,88585,1333731,22602020,420261225,8536210843,
%T A356595 187294058787,4420961159582,111409233290537,2986570482052729,
%U A356595 84773698697674837,2539347801355477960,80003306259203052465,2644032803825175398175,91425359712959262036223
%N A356595 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k)^k )^exp(x).
%F A356595 a(0) = 1; a(n) = Sum_{k=1..n} A356600(k) * binomial(n-1,k-1) * a(n-k).
%o A356595 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^k)^exp(x)))
%o A356595 (PARI) a356600(n) = n!*sum(k=1, n, sigma(k, 2)/(k*(n-k)!));
%o A356595 a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356600(j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A356595 Cf. A346545, A346547.
%Y A356595 Cf. A356337, A356600.
%K A356595 nonn
%O A356595 0,3
%A A356595 _Seiichi Manyama_, Aug 15 2022