OFFSET
0,2
LINKS
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+3,k) * binomial(3*n-3*k+1,n-3*k).
a(n) = (1/(n+1)) * [x^n] ( 1/(1-x)^2 * (1+x^3)^3 )^(n+1). - Seiichi Manyama, Feb 14 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2/(1+x^3)^3)/x)
(PARI) a(n, s=3, t=3, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 18 2024
STATUS
approved