A359649 a(n) = hypergeom([(1 - n)/2, -n/2], [2], 4*n^2).

1, 1, 5, 28, 609, 6501, 272701, 4286815, 272156417, 5648748355, 484054204501, 12482361156398, 1351553781736225, 41650209565275195, 5460281206077347469, 195722005810272604876, 30156361094764202326017, 1232550298298392183231275, 218366864894707599746619685

Offset: 0

Author

Peter Luschny, Jan 10 2023

Keywords

• nonn

Crossrefs

Cf. A359364.

Programs

Maple

a := n -> hypergeom([(1 - n)/2, -n/2], [2], 4*n^2):
seq(simplify(a(n)), n = 0..18);

Formula

a(n) = p(n, n), where p(n, x) = hypergeom([(1 - n)/2, -n/2], [2], (2*x)^2) are the Motzkin polynomials A359364.

a(n) ~ (exp(1) + (-1)^n) * 2^(n + 1/2) * n^(n - 3/2) / (sqrt(Pi) * exp(1/2)). - Vaclav Kotesovec, Jan 08 2024