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%I #5 Nov 07 2021 02:37:07
%S 1,1,-7,-239,30185,15518977,-31752293287,-260178568173071,
%T 8525011498792301513,1117407361630407158712289,
%U -585841036144574163016069731271,-1228598872333737909217248906305521967,10306231872061986643099600924851012311829929
%N G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(-4*x)).
%F a(0) = 1; a(n) = -a(n-1) + 2 * Sum_{k=0..n-1} (-4)^k * a(k) * a(n-k-1).
%t nmax = 12; A[_] = 0; Do[A[x_] = 1/(1 + x - 2 x A[-4 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = 1; a[n_] := a[n] = -a[n - 1] + 2 Sum[(-4)^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 12}]
%Y Cf. A001003, A015099, A348902, A349038, A349045.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Nov 06 2021
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