OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} 5^(n-k) * binomial(2*n+k+1,k) * binomial(2*n,n-k).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-6*x)^2/(1-5*x))/x)
(PARI) a(n) = sum(k=0, n, 5^(n-k)*binomial(2*n+k+1, k)*binomial(2*n, n-k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 19 2024
STATUS
approved