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%I #6 Nov 02 2021 09:50:38
%S 1,2,11,204,13701,3550838,3646912991,14948746703872,
%T 244965160945456921,16054771878797715999594,
%U 4208710286900635084866205491,4413165224136772109314051383922356,18510169791808150609141704979384516863021,310549172324407121253872529077196811473762678750
%N G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(4*x))).
%F a(n) = 1 + Sum_{k=0..n-1} 4^k * a(k) * a(n-k-1).
%F a(n) ~ c * 2^(n*(n-1)), where c = 3.399782064170449155365557063612838469541502782488369640092639686931819... - _Vaclav Kotesovec_, Nov 02 2021
%t nmax = 13; A[_] = 0; Do[A[x_] = 1/((1 - x) (1 - x A[4 x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[n_] := a[n] = 1 + Sum[4^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]
%Y Cf. A007317, A015085, A348857, A348858.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Nov 02 2021
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