A377145 a(n) = Sum_{k=0..n} binomial(k+2,2) * binomial(k,n-k)^2.

1, 3, 9, 34, 111, 351, 1103, 3384, 10224, 30536, 90222, 264186, 767663, 2215623, 6356907, 18143300, 51540885, 145801395, 410888595, 1153964520, 3230723826, 9019081038, 25112021154, 69750583164, 193303849531, 534602071341, 1475644537323, 4065845732794

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

G.f.: ((1-x-x^2)^2 + 2*x^3) / ((1-x-x^2)^2 - 4*x^3)^(5/2).

Prog

(PARI) a(n) = sum(k=0, n, binomial(k+2, 2)*binomial(k, n-k)^2);
(PARI) a089627(n, k) = n!/((n-2*k)!*k!^2);
my(N=2, 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))

Crossrefs

Cf. A051286, A182884, A377148, A377152, A377153, A377158, A377159.

Cf. A377146, A377147.

Cf. A089627.

Sequence in context: A138769 A100076 A213907 * A148999 A149000 A160963

Adjacent sequences: A377142 A377143 A377144 * A377146 A377147 A377148

Keyword

nonn

Author

Seiichi Manyama, Oct 17 2024

Status

approved