A348862 G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(4*x))).

1, 0, 1, 16, 1041, 267552, 274242081, 1123570105392, 18409696460431921, 1206516278059945211200, 316282209730469497179053121, 331646250633753603369328903503952, 1391025527264722227030105092707830630481, 23337537123459992903665202300959789335795178848

Offset: 0

Author

Ilya Gutkovskiy, Nov 02 2021

Keywords

• nonn

Crossrefs

Cf. A005043, A015085, A348860, A348861.

Programs

Mathematica

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]
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}]

Formula

a(n) = (-1)^n + Sum_{k=0..n-1} 4^k * a(k) * a(n-k-1).

a(n) ~ c * 2^(n*(n-1)), where c = 0.2554910592341818819974992745952574870516320592891123415106817713508566833... - Vaclav Kotesovec, Nov 02 2021