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A363440 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (4*x)^k/k ).

%I A363440 #12 Jun 03 2023 09:01:48
%S A363440 1,4,32,256,2208,19712,183808,1763328,17332992,173621248,1766188288,
%T A363440 18196260864,189474570240,1990887063552,21082432966656,
%U A363440 224766598100992,2410570956881920,25988893875994624,281505478557407232,3062014088362049536
%N A363440 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (4*x)^k/k ).
%H A363440 Seiichi Manyama, <a href="/A363440/b363440.txt">Table of n, a(n) for n = 0..938</a>
%F A363440 A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-4*x^(k+1))^a(k).
%F A363440 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 A363440 (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, subst(A, x, x^k)*(4*x)^k/k)+x*O(x^n))); Vec(A);
%Y A363440 Cf. A000081, A179469, A363439.
%Y A363440 Cf. A363424.
%K A363440 nonn
%O A363440 0,2
%A A363440 _Seiichi Manyama_, Jun 02 2023