A384300 a(n) = Product_{k=0..2*n-1} (3*n+k-2).

1, 2, 840, 665280, 980179200, 2346549004800, 8326896754176000, 41098950018846720000, 269397128065642536960000, 2264501147602213494374400000, 23751156416080627455365283840000, 304080322557324667642345606348800000, 4667216066941750219330172809445376000000

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

a(n) = RisingFactorial(3*n-2,2*n).

a(n) = (2*n)! * [x^(2*n)] 1/(1 - x)^(3*n-2).

a(n) = (2*n)! * binomial(5*n-3,2*n).

D-finite with recurrence 3*(3*n-4)*(3*n-5)*a(n) - 5*(5*n-4)*(5*n-3)*(5*n-7)*(5*n-6)*a(n-1) = 0. - R. J. Mathar, May 26 2025

a(n) ~ 5^(5*n-5/2) * (n/e)^(2*n) / 3^(3*n-5/2). - Amiram Eldar, Nov 06 2025

Mathematica

a[n_] := (2*n)! * Binomial[5*n - 3, 2*n]; Array[a, 13, 0] (* Amiram Eldar, Nov 06 2025 *)

Prog

(PARI) a(n) = (2*n)!*binomial(5*n-3, 2*n);

Crossrefs

Cf. A384301, A384302, A384303.

Cf. A384262.

Sequence in context: A109555 A214898 A332182 * A230396 A028485 A034227

Adjacent sequences: A384297 A384298 A384299 * A384301 A384302 A384303

Keyword

nonn,easy

Author

Seiichi Manyama, May 25 2025

Status

approved