OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(3*n-k+3,n-3*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+x+x^3)))/x)
(PARI) a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 23 2024
STATUS
approved