A350467 a(n) = hypergeom([1/2 - n/2, -n/2], [-n], -8*n).

1, 1, 5, 13, 89, 341, 2653, 13021, 110449, 648469, 5891381, 39734685, 382729801, 2887493077, 29287115341, 242592910621, 2577978650081, 23125601566165, 256460946182821, 2465492129670493, 28441473938165561, 290630718826209301, 3477967327342044989, 37528922270996471133

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = Sum_{k=0..n} binomial(n - k, k)*(2*n)^k.

a(n) = A350470(n, n).

From Vaclav Kotesovec, Jan 08 2024: (Start)

a(n) = ((1 + sqrt(8*n+1))^(n+1) - (1 - sqrt(8*n+1))^(n+1)) / (sqrt(8*n+1) * 2^(n+1)).

a(n) ~ exp(sqrt(n/2)/2) * 2^(n/2 - 1) * n^(n/2) * (1 + 47/(96*sqrt(2*n))). (End)

Mathematica

Table[Hypergeometric2F1[(1 - n)/2, -n/2, -n, -8 n ], {n, 0, 23}]
Table[FullSimplify[((1 + Sqrt[8*n + 1])^(n+1) - (1 - Sqrt[8*n + 1])^(n+1)) / (Sqrt[8*n + 1] * 2^(n+1))], {n, 0, 25}] (* Vaclav Kotesovec, Jan 08 2024 *)

Crossrefs

Cf. A171180, A350470.

Sequence in context: A092955 A190949 A263468 * A081560 A057624 A092567

Adjacent sequences: A350464 A350465 A350466 * A350468 A350469 A350470

Keyword

nonn

Author

Peter Luschny, Mar 19 2022

Status

approved