OFFSET
0,3
COMMENTS
Satisfies a 7-term D-finite recurrence with 7-order polynomials. - R. J. Mathar, Jan 25 2024
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} 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, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 11 2024
STATUS
approved