OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(2*n+2*k+2,n-3*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1+x)^2-x^3))/x)
(PARI) a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(2*n+2*k+2, n-3*k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 27 2024
STATUS
approved