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%I #6 Nov 02 2021 09:52:16
%S 1,0,1,16,1041,267552,274242081,1123570105392,18409696460431921,
%T 1206516278059945211200,316282209730469497179053121,
%U 331646250633753603369328903503952,1391025527264722227030105092707830630481,23337537123459992903665202300959789335795178848
%N G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(4*x))).
%F a(n) = (-1)^n + Sum_{k=0..n-1} 4^k * a(k) * a(n-k-1).
%F a(n) ~ c * 2^(n*(n-1)), where c = 0.2554910592341818819974992745952574870516320592891123415106817713508566833... - _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)^n + Sum[4^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]
%Y Cf. A005043, A015085, A348860, A348861.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Nov 02 2021
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