A386898 a(n) = Sum_{k=0..n} binomial(5*n+1,k) * binomial(5*n-k,n-k).

1, 11, 199, 4031, 85919, 1885311, 42154111, 955020287, 21847988735, 503573013503, 11675986431999, 272033089535999, 6363380561141759, 149354395882487807, 3515589114309115903, 82957940541503045631, 1961823306198598418431, 46482660516543479939071

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = [x^n] (1+x)^(5*n+1)/(1-x)^(4*n+1).

a(n) = [x^n] 1/((1-x) * (1-2*x)^(4*n+1)).

a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(5*n+1,k).

a(n) = Sum_{k=0..n} 2^k * binomial(4*n+k,k).

a(n) = binomial(5*n, n)*hypergeom([-1-5*n, -n], [-5*n], -1). - Stefano Spezia, Aug 07 2025

Prog

(PARI) a(n) = sum(k=0, n, binomial(5*n+1, k)*binomial(5*n-k, n-k));

Crossrefs

Cf. A386812, A386895, A386896, A386897.

Cf. A178792, A383326, A383716.

Sequence in context: A112733 A088295 A305316 * A352842 A268959 A213531

Adjacent sequences: A386895 A386896 A386897 * A386899 A386900 A386901

Keyword

nonn

Author

Seiichi Manyama, Aug 07 2025

Status

approved