A377159 a(n) = Sum_{k=0..n} binomial(k+7,7) * binomial(k,n-k)^2.

1, 8, 44, 264, 1446, 7152, 33516, 149688, 640233, 2642992, 10582220, 41249000, 157050660, 585621960, 2143442400, 7715164176, 27353809188, 95660348904, 330377130644, 1127996393656, 3810881349814, 12750188169312, 42276102419916, 139008143200536, 453526927536969

Offset: 0

Author

Seiichi Manyama, Oct 18 2024

Keywords

• nonn

Crossrefs

Cf. A051286, A182884, A377145, A377148, A377152, A377153, A377158.

Cf. A089627.

Programs

PARI

a(n) = sum(k=0, n, binomial(k+7, 7)*binomial(k, n-k)^2);

PARI

a089627(n, k) = n!/((n-2*k)!*k!^2);
my(N=7, 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(7,k) * (1-x-x^2)^(7-2*k) * x^(3*k)) / ((1-x-x^2)^2 - 4*x^3)^(15/2).