OFFSET
0,3
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
MAPLE
a := n -> hypergeom([(1 - n)/2, -n/2], [2], 4*n^2):
seq(simplify(a(n)), n = 0..18);
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Jan 10 2023
STATUS
approved