OFFSET
0,3
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(3*n+k+2,k) * binomial(n-k-1,n-2*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1+x^2/(1-x))^3)/x)
(PARI) a(n, s=2, t=3, u=-3) = sum(k=0, n\s, (-1)^k*binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jan 12 2024
STATUS
approved