OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} 3^k * binomial(n+k,k) * binomial(4*n+k+2,n-2*k).
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} 3^(n-3*k) * binomial(n+k,k) * binomial(2*n-2*k,n-3*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-3*x-x^3))/x)
(PARI) a(n) = sum(k=0, n\2, 3^k*binomial(n+k, k)*binomial(4*n+k+2, n-2*k))/(n+1);
(PARI) a(n) = sum(k=0, n\3, 3^(n-3*k)*binomial(n+k, k)*binomial(2*n-2*k, n-3*k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 23 2024
STATUS
approved