A377146 a(n) = Sum_{k=0..floor(n/2)} binomial(k+2,2) * binomial(k,n-2*k)^2.

1, 0, 3, 3, 6, 24, 16, 90, 105, 250, 561, 765, 2143, 3108, 6861, 12985, 22221, 47988, 79463, 161451, 293610, 535836, 1042188, 1835898, 3534766, 6399198, 11805756, 22021232, 39718497, 74193924, 134489713, 247165839, 453235266, 822748406, 1512078192, 2741606052

Offset: 0

Author

Seiichi Manyama, Oct 17 2024

Keywords

• nonn

Crossrefs

Cf. A377145, A377147.

Cf. A298567, A375218.

Cf. A089627.

Programs

PARI

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

PARI

a089627(n, k) = n!/((n-2*k)!*k!^2);
my(N=2, 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))

Formula

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