A377158 a(n) = Sum_{k=0..n} binomial(k+6,6) * binomial(k,n-k)^2.

1, 7, 35, 196, 994, 4578, 20118, 84540, 341397, 1335103, 5078227, 18852428, 68519920, 244413820, 857393700, 2963013816, 10102413972, 34025396580, 113329367816, 373642488044, 1220412680410, 3951964394642, 12695738508950, 40484919514284, 128216539026261

Offset: 0

Author

Seiichi Manyama, Oct 18 2024

Keywords

• nonn

Crossrefs

Cf. A051286, A182884, A377145, A377148, A377152, A377153, A377159.

Cf. A089627.

Programs

PARI

a(n) = sum(k=0, n, binomial(k+6, 6)*binomial(k, n-k)^2);

PARI

a089627(n, k) = n!/((n-2*k)!*k!^2);
my(N=6, M=30, x='x+O('x^M), X=1-x-x^2, Y=3); Vec(sum(k=0, N\2, a089627(N, k)*X^(N-2*k)*x^(Y*k))/(X^2-4*x^Y)^(N+1/2))

Formula

G.f.: (Sum_{k=0..3} A089627(6,k) * (1-x-x^2)^(6-2*k) * x^(3*k)) / ((1-x-x^2)^2 - 4*x^3)^(13/2).