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G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (4*x)^k/k ).
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%I #15 Jun 03 2023 09:01:54

%S 1,4,16,128,864,6912,55936,470016,4025600,35144704,311190784,

%T 2789206016,25254028288,230652174336,2122466561024,19659305379840,

%U 183146187440128,1714933158969344,16131631511164928,152366562180972544

%N G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (4*x)^k/k ).

%H Seiichi Manyama, <a href="/A363443/b363443.txt">Table of n, a(n) for n = 0..996</a>

%F A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+4*x^(k+1))^a(k).

%F a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-4)^(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, (-1)^(k+1)*subst(A, x, x^k)*(4*x)^k/k)+x*O(x^n))); Vec(A);

%Y Cf. A004111, A363441, A363442.

%Y Cf. A363427, A363440.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 02 2023