A384301 a(n) = Product_{k=0..2*n-1} (3*n+k-1).

1, 6, 1680, 1235520, 1764322560, 4151586700800, 14572069319808000, 71382386874839040000, 465322312113382563840000, 3894941973875807210323968000, 40716268141852504209197629440000, 519879261146393786614332810854400000, 7961721525959456256504412439642112000000

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

D-finite with recurrence 3*(3*n-2)*(3*n-4)*a(n) - 5*(5*n-4)*(5*n-3)*(5*n-2)*(5*n-6)*a(n-1) = 0. - R. J. Mathar, May 26 2025

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

Mathematica

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

Prog

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

Crossrefs

Cf. A384300, A384302, A384303.

Cf. A384263.

Sequence in context: A308029 A160226 A209609 * A350595 A034841 A149187

Adjacent sequences: A384298 A384299 A384300 * A384302 A384303 A384304

Keyword

nonn,easy

Author

Seiichi Manyama, May 25 2025

Status

approved