Voozh

A358114

a(n) = [x^n] (16*x*(32*x - 3) + 1)^(-1/2).

1, 24, 608, 16128, 443904, 12570624, 363708416, 10694295552, 318301929472, 9562594738176, 289380790960128, 8807948507676672, 269349580129173504, 8268747111256817664, 254668380196759928832, 7865254221563736096768, 243493498808268962660352, 7553805204299934842486784

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = 16^n * hypergeom([1/2, -n], [1], -1).

D-finite with recurrence a(n) = (24*(2*n - 1)*a(n - 1) - 512*(n - 1)*a(n - 2)) / n for n >= 2.

a(n) ~ 2^(5*n + 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Nov 12 2022

a(n) = 4^n*A098410(n). - R. J. Mathar, Jan 25 2023

MAPLE

ogf := (16*x*(32*x - 3) + 1)^(-1/2): ser := series(ogf, x, 20):