OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} 4^k * binomial(n/2+k-1/2,k) * binomial(k,n-k).
a(n) = 4^n*binomial((3*n-1)/2, n)*hypergeom([(1-n)/2, -n/2], [(1-3*n)/2], -1)/(n+1). - Stefano Spezia, Apr 18 2024
PROG
(PARI) a(n) = sum(k=0, n, 4^k*binomial(n/2+k-1/2, k)*binomial(k, n-k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 17 2024
STATUS
approved