OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 1/sqrt(1 - 4 * x^2 * (1+x)^2).
a(n) = Sum_{k=0..floor(n/2)} binomial(2*k,k) * binomial(2*k,n-2*k).
a(n) ~ (1 + sqrt(3))^(n + 1/2) / (2*3^(1/4)*sqrt(Pi*n)). - Vaclav Kotesovec, Mar 22 2023
n*a(n) = 2*(2*n-2)*a(n-2) + 4*(2*n-3)*a(n-3) + 2*(2*n-4)*a(n-4) for n > 3. - Seiichi Manyama, Mar 23 2023
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(2*k, k)*binomial(2*k, n-2*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 22 2023
STATUS
approved