A358117 a(n) = 64^n * hypergeom([-1/2, -1/2, -1/2, -n], [1, 1, 1], 1).

1, 72, 5112, 358976, 24984600, 1726182336, 118527759552, 8095995597312, 550493745978456, 37283830177899200, 2516416350265032768, 169320882931135520256, 11361845611339758248896, 760535818250019673548288, 50795721177620909117683200, 3385797370455910806595080192

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*(24*n^3 - 12*n^2 - 22*n + 19)*a(n-1) - 3072*(n-1)*(4*n^2 - 7)*a(n-2) + 131072*(n-2)*(n-1)*(2*n + 3)*a(n-3).

a(n) ~ 64^n * log(n)^2 * sqrt(n) / Pi^(5/2) * (1 + c1/log(n) + c2/log(n)^2), where c1 = -3.755213781237809328111261876504370048707679178356... and c2 = 14.59060543515491211393377346917067214120336575838... (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, A358116.

Sequence in context: A054557 A167871 A103861 * A358116 A216705 A223148

Adjacent sequences: A358114 A358115 A358116 * A358118 A358119 A358120

Keyword

nonn

Author

Peter Luschny, Nov 12 2022

Status

approved