OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+2,k) * binomial(6*n-3*k+6,n-3*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3+x^3)^2)/x)
(PARI) a(n) = sum(k=0, n\3, binomial(2*n+2, k)*binomial(6*n-3*k+6, n-3*k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 25 2024
STATUS
approved