cp's OEIS Frontend

A363565 G.f. satisfies A(x) = exp( Sum_{k>=1} (2 * (-1)^k + A(x^k)) * x^k/k ).

%I A363565 #10 Jun 10 2023 11:18:21
%S A363565 1,-1,1,0,0,0,1,0,0,1,1,0,1,2,2,1,3,5,4,4,10,13,11,16,30,34,35,58,91,
%T A363565 99,123,200,275,315,437,671,869,1065,1548,2239,2848,3730,5446,7530,
%U A363565 9699,13273,19056,25730,33947,47463,66796,89565,120976,170033,235524
%N A363565 G.f. satisfies A(x) = exp( Sum_{k>=1} (2 * (-1)^k + A(x^k)) * x^k/k ).
%F A363565 A(x) = B(x)/(1 + x)^2 where B(x) is the g.f. of A363567.
%F A363565 A(x) = Sum_{k>=0} a(k) * x^k = 1/(1+x)^2 * 1/Product_{k>=0} (1-x^(k+1))^a(k).
%F A363565 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( 2 * (-1)^k + Sum_{d|k} d * a(d-1) ) * a(n-k).
%o A363565 (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (2*(-1)^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
%Y A363565 Cf. A001678, A363566.
%Y A363565 Cf. A363567.
%K A363565 sign
%O A363565 0,14
%A A363565 _Seiichi Manyama_, Jun 10 2023