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

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):
seq(coeff(ser, x, n), n = 0..17);

Mathematica

a[n_] := 16^n * HypergeometricPFQ[{1/2, -n}, {1}, -1]; Array[a, 18, 0] (* Amiram Eldar, Nov 12 2022 *)

Crossrefs

Cf. A098430.

Sequence in context: A001806 A144348 A167870 * A097192 A182611 A331322

Adjacent sequences: A358111 A358112 A358113 * A358115 A358116 A358117

Keyword

nonn

Author

Peter Luschny, Nov 12 2022

Status

approved