OFFSET
0,3
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-3*k+1,k) * binomial(2*n-3*k,n-3*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1-x^3)-x))/x)
(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-3*k+1, k)*binomial(2*n-3*k, n-3*k))/(n+1);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Mar 03 2024
STATUS
approved