A377149 a(n) = Sum_{k=0..floor(n/2)} binomial(k+3,3) * binomial(k,n-2*k)^2.

1, 0, 4, 4, 10, 40, 30, 180, 215, 580, 1316, 1960, 5719, 8624, 20420, 39536, 71985, 160584, 276664, 588180, 1099786, 2098480, 4201594, 7665724, 15266640, 28422684, 54252560, 103928876, 193166861, 371012360, 690296162, 1304353740, 2450895828, 4565652908

Offset

0,3

Links

Table of n, a(n) for n=0..33.

Formula

G.f.: (1-x^2-x^3) * ((1-x^2-x^3)^2 + 6*x^5) / ((1-x^2-x^3)^2 - 4*x^5)^(7/2).

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(k+3, 3)*binomial(k, n-2*k)^2);
(PARI) a089627(n, k) = n!/((n-2*k)!*k!^2);
my(N=3, M=40, x='x+O('x^M), X=1-x^2-x^3, Y=5); 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. A377148, A377150.

Cf. A089627.

Sequence in context: A117881 A373101 A342989 * A161719 A343090 A161433

Adjacent sequences: A377146 A377147 A377148 * A377150 A377151 A377152

Keyword

nonn

Author

Seiichi Manyama, Oct 18 2024

Status

approved