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G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} A(-x^k) * x^k/k ).
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%I #17 Jun 04 2023 11:47:23

%S 1,2,-1,-6,7,42,-58,-366,513,3406,-4846,-33310,48304,339446,-499133,

%T -3565468,5294439,38312242,-57332347,-419177900,631252549,4654229300,

%U -7045498256,-52310262192,79531957334,593986308994,-906439292326,-6803984285256

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

%H Seiichi Manyama, <a href="/A363470/b363470.txt">Table of n, a(n) for n = 0..1000</a>

%F A(x) = B(x)^2 where B(x) is the g.f. of A200438.

%F A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(k+1))^(2 * (-1)^k * a(k)).

%F 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 (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 Cf. A000151, A200438, A363471.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jun 03 2023