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A359649
a(n) = hypergeom([(1 - n)/2, -n/2], [2], 4*n^2).
1
1, 1, 5, 28, 609, 6501, 272701, 4286815, 272156417, 5648748355, 484054204501, 12482361156398, 1351553781736225, 41650209565275195, 5460281206077347469, 195722005810272604876, 30156361094764202326017, 1232550298298392183231275, 218366864894707599746619685
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
Cf. A359364.
Sequence in context: A024068 A308593 A249784 * A346312 A359739 A344464
KEYWORD
nonn
AUTHOR
Peter Luschny, Jan 10 2023
STATUS
approved