%I #7 Jan 08 2024 07:58:41
%S 1,1,5,28,609,6501,272701,4286815,272156417,5648748355,484054204501,
%T 12482361156398,1351553781736225,41650209565275195,
%U 5460281206077347469,195722005810272604876,30156361094764202326017,1232550298298392183231275,218366864894707599746619685
%N a(n) = hypergeom([(1 - n)/2, -n/2], [2], 4*n^2).
%F a(n) = p(n, n), where p(n, x) = hypergeom([(1 - n)/2, -n/2], [2], (2*x)^2) are the Motzkin polynomials A359364.
%F a(n) ~ (exp(1) + (-1)^n) * 2^(n + 1/2) * n^(n - 3/2) / (sqrt(Pi) * exp(1/2)). - _Vaclav Kotesovec_, Jan 08 2024
%p a := n -> hypergeom([(1 - n)/2, -n/2], [2], 4*n^2):
%p seq(simplify(a(n)), n = 0..18);
%Y Cf. A359364.
%K nonn
%O 0,3
%A _Peter Luschny_, Jan 10 2023