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A363470 G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} A(-x^k) * x^k/k ).

%I A363470 #17 Jun 04 2023 11:47:23
%S A363470 1,2,-1,-6,7,42,-58,-366,513,3406,-4846,-33310,48304,339446,-499133,
%T A363470 -3565468,5294439,38312242,-57332347,-419177900,631252549,4654229300,
%U A363470 -7045498256,-52310262192,79531957334,593986308994,-906439292326,-6803984285256
%N A363470 G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} A(-x^k) * x^k/k ).
%H A363470 Seiichi Manyama, <a href="/A363470/b363470.txt">Table of n, a(n) for n = 0..1000</a>
%F A363470 A(x) = B(x)^2 where B(x) is the g.f. of A200438.
%F A363470 A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(k+1))^(2 * (-1)^k * a(k)).
%F A363470 a(0) = 1; a(n) = (2/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-1)^(d-1) * a(d-1) ) * a(n-k).
%o A363470 (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(2*sum(k=1, i, subst(A, x, -x^k)*x^k/k)+x*O(x^n))); Vec(A);
%Y A363470 Cf. A000151, A200438, A363471.
%K A363470 sign
%O A363470 0,2
%A A363470 _Seiichi Manyama_, Jun 03 2023