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%I #23 Jul 25 2023 08:17:49
%S 1,1,4,36,640,21888,1451008,188941312,48768745472,25069815595008,
%T 25722272102744064,52730972085034156032,216091838647321476726784,
%U 1770657164881170759078117376,29013990909330956353981535748096
%N G.f. satisfies A(x) = 1 + x*A(2*x)^2.
%C Self-convolution equals A135868 such that 2^n*A135868(n) = a(n+1) for n >= 0.
%H Seiichi Manyama, <a href="/A135867/b135867.txt">Table of n, a(n) for n = 0..81</a>
%F a(n) = 2^(n-1)*Sum_{k=0..n-1} a(k)*a(n-k-1) for n>0 with a(0)=1. - _Paul D. Hanna_, Feb 09 2010
%F a(n) ~ c * 2^(n*(n+1)/2), where c = 0.715337433614869740944075474484711589980951273610257702786245519231799678... - _Vaclav Kotesovec_, Nov 04 2021
%t nmax = 15; A[_] = 0; Do[A[x_] = 1 + x*A[2*x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* _Vaclav Kotesovec_, Nov 04 2021 *)
%o (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=0,n,A=1+x*subst(A,x,2*x)^2);polcoeff(A,n)}
%o (PARI) a(n)=if(n==0,1,2^(n-1)*sum(k=0,n-1,a(k)*a(n-k-1))) \\ _Paul D. Hanna_, Feb 09 2010
%Y Cf. A015083, A135868, A171192.
%Y Cf. A171200, A171202, A171204, A171206, A171208, A171210, A343439.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 02 2007
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