A358116 a(n) = 64^n * hypergeometric([1/2, 1/2, 1/2, -n], [1, 1, 1], -1).

1, 72, 5336, 409920, 32865240, 2764504512, 244568268224, 22731850578432, 2210652884587480, 223568522839008960, 23355989488375500096, 2504727132759950771712, 274275125399986388723136, 30537418979006689934661120, 3445701451953128810934443520, 393048128243054017436740669440

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

From Vaclav Kotesovec, Feb 17 2024: (Start)

Recurrence: n^3*a(n) = 8*(2*n - 1)*(20*n^2 - 20*n + 9)*a(n-1) - 1024*(n-1)*(36*n^2 - 72*n + 41)*a(n-2) + 917504*(n-2)*(n-1)*(2*n - 3)*a(n-3) - 33554432*(n-3)*(n-2)*(n-1)*a(n-4).

a(n) ~ 2^(7*n + 3/2) / (Pi^(3/2) * n^(3/2)). (End)

Maple

a := n -> 64^n*hypergeom([1/2, 1/2, 1/2, -n], [1, 1, 1], -1):
seq(simplify(a(n)), n = 0..15);

Mathematica

a[n_] := 64^n * HypergeometricPFQ[{1/2, 1/2, 1/2, -n}, {1, 1, 1}, -1]; Array[a, 16, 0] (* Amiram Eldar, Nov 12 2022 *)

Crossrefs

Cf. A358115, A358117.

Sequence in context: A167871 A103861 A358117 * A216705 A223148 A289368

Adjacent sequences: A358113 A358114 A358115 * A358117 A358118 A358119

Keyword

nonn

Author

Peter Luschny, Nov 12 2022

Status

approved