OFFSET
0,3
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(4*n+k+3,k) * binomial(6*n-k+4,n-k).
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(4*n+k+3,k) * binomial(2*n-2*k,n-2*k). - Seiichi Manyama, Jan 18 2024
a(n) = (1/(n+1)) * [x^n] 1/( (1+x)^4 * (1-x)^5 )^(n+1). - Seiichi Manyama, Feb 16 2024
PROG
(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(4*n+k+3, k)*binomial(6*n-k+4, n-k))/(n+1);
(SageMath)
def A365880(n):
h = binomial(6*n + 4, n) * hypergeometric([-n, 4*(n + 1)], [-6 * n - 4], -1) / (n + 1)
return simplify(h)
print([A365880(n) for n in range(23)]) # Peter Luschny, Sep 21 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 21 2023
STATUS
approved