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%I #9 Jun 10 2023 11:18:26
%S 1,-2,2,0,-2,0,5,-3,-9,11,16,-34,-27,102,30,-296,56,807,-548,-2056,
%T 2572,4770,-9846,-9351,33822,11496,-107296,17853,316498,-210013,
%U -862785,1069352,2122294,-4347217,-4402138,15657617,5883290,-51677928,7420844,157867636
%N G.f. satisfies A(x) = exp( Sum_{k>=1} (3 * (-1)^k + A(x^k)) * x^k/k ).
%F A(x) = B(x)/(1 + x)^3 where B(x) is the g.f. of A363575.
%F A(x) = Sum_{k>=0} a(k) * x^k = 1/(1+x)^3 * 1/Product_{k>=0} (1-x^(k+1))^a(k).
%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( 3 * (-1)^k + Sum_{d|k} d * a(d-1) ) * a(n-k).
%o (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (3*(-1)^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
%Y Cf. A001678, A363565.
%Y Cf. A363509, A363575.
%K sign
%O 0,2
%A _Seiichi Manyama_, Jun 10 2023
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