A384303 a(n) = Product_{k=0..2*n-1} (3*n+k+1).

1, 20, 5040, 3603600, 5079110400, 11861676288000, 41430393164160000, 202250096145377280000, 1315041316842168115200000, 10985733772470225465016320000, 114660755112113373922453094400000, 1462160421974232524852811030528000000, 22368646191981329482560015901851648000000

Offset

0,2

Links

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

Formula

a(n) = RisingFactorial(3*n+1,2*n).

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

a(n) = (5*n)!/(3*n)!.

D-finite with recurrence 3*(3*n-1)*(3*n-2)*a(n) - 5*(5*n-4)*(5*n-3)*(5*n-2)*(5*n-1)*a(n-1) = 0. - R. J. Mathar, May 26 2025

a(n) ~ 5^(5*n+1/2) * (n/e)^(2*n) / 3^(3*n+1/2). - Amiram Eldar, Nov 06 2025

Mathematica

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

Prog

(PARI) a(n) = (5*n)!/(3*n)!;

Crossrefs

Cf. A384300, A384301, A384302.

Cf. A166384.

Sequence in context: A279297 A079759 A109894 * A227765 A250020 A088852

Adjacent sequences: A384300 A384301 A384302 * A384304 A384305 A384306

Keyword

nonn,easy

Author

Seiichi Manyama, May 25 2025

Status

approved