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%I #15 Jul 25 2023 08:17:30
%S 1,1,6,84,2312,121056,12173568,2391143424,928316362752,
%T 716762538541056,1103851068987015168,3395472896229407981568,
%U 20875407961847891162038272,256600638160251032545689337856,6307244441266548036155317187248128
%N G.f. satisfies A(x) = 1 + x*A(2x)^3.
%H Seiichi Manyama, <a href="/A171200/b171200.txt">Table of n, a(n) for n = 0..80</a>
%F a(0) = 1; a(n) = 2^(n-1) * Sum_{i=0..n-1} Sum_{j=0..n-i-1} a(i) * a(j) * a(n-i-j-1). - _Ilya Gutkovskiy_, Nov 03 2021
%t m = 15; A[_] = 0; Do[A[x_] = 1 + x A[2x]^3 + O[x]^m // Normal, {m}];
%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Nov 07 2019 *)
%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^3); polcoeff(A, n)}
%Y Cf. A135867, A171201, A171202-A171211, A343439.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 05 2009
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