OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(n+k,k) * binomial(4*n-k+2,n-k).
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+k,k) * binomial(3*n-2*k+1,n-2*k). - Seiichi Manyama, Jan 18 2024
a(n) = (1/(n+1)) * [x^n] 1/( (1+x) * (1-x)^3 )^(n+1). - Seiichi Manyama, Feb 16 2024
PROG
(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+k, k)*binomial(4*n-k+2, n-k))/(n+1);
(SageMath)
def A365751(n):
h = binomial(4*n + 2, n) * hypergeometric([-n, n + 1], [-4 * n - 2], -1) / (n + 1)
return simplify(h)
print([A365751(n) for n in range(23)]) # Peter Luschny, Sep 20 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 18 2023
STATUS
approved