A358115 a(n) = 64^n * hypergeometric([1/2, 1/2, 1/2, -n], [1, 1, 1], 1).

1, 56, 3288, 197312, 11992024, 734961216, 45312662976, 2806150276608, 174385474327512, 10867238335817024, 678767129043750208, 42476876703235742208, 2662498434919062169024, 167121637293079702800896, 10502764033533202152955392, 660751064709823030602903552

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)*(12*n^2 - 12*n + 7)*a(n-1) - 3072*(n-1)*(4*n^2 - 8*n + 5)*a(n-2) + 131072*(n-2)*(n-1)*(2*n - 3)*a(n-3).

a(n) ~ 2^(6*n-1) * log(n)^2 / (Pi^(5/2)*sqrt(n)) * (1 + c1/log(n) + c2/log(n)^2), where c1 = 12.24478621876219067188873812349562995129232082... and c2 = 32.54889518525243748904367845713571175154193233... (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. A358116, A358117.

Sequence in context: A224021 A042513 A264941 * A216704 A278724 A277770

Adjacent sequences: A358112 A358113 A358114 * A358116 A358117 A358118

Keyword

nonn

Author

Peter Luschny, Nov 12 2022

Status

approved