A377147 a(n) = Sum_{k=0..floor(n/3)} binomial(k+2,2) * binomial(k,n-3*k)^2.

1, 0, 0, 3, 3, 0, 6, 24, 6, 10, 90, 90, 25, 240, 540, 261, 540, 2100, 2128, 1533, 6321, 11236, 8064, 16884, 44173, 46980, 51156, 142939, 224991, 212400, 423426, 882660, 1006875, 1338558, 2991318, 4431669, 5034296, 9457704, 17178678, 21059737, 30809286, 59843394, 86518266

Offset: 0

Author

Seiichi Manyama, Oct 17 2024

Keywords

• nonn

Crossrefs

Cf. A377145, A377146.

Cf. A375470, A376721.

Cf. A089627.

Programs

PARI

a(n) = sum(k=0, n\3, binomial(k+2, 2)*binomial(k, n-3*k)^2);

PARI

a089627(n, k) = n!/((n-2*k)!*k!^2);
my(N=2, M=50, x='x+O('x^M), X=1-x^3-x^4, Y=7); 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.: ((1-x^3-x^4)^2 + 2*x^7) / ((1-x^3-x^4)^2 - 4*x^7)^(5/2).