A248707 a(n) = f(3*n)/(f(n-1)*f(n)*f(n+1)), where f(k) = k!.

3, 60, 1260, 27720, 630630, 14702688, 349188840, 8413788240, 205086088350, 5046360719400, 125149745841120, 3124367780788800, 78443948210518800, 1979201154850012800, 50151543548788717200, 1275619260617425959840, 32554866547007225016750, 833323952354971320243000

Offset: 1

Author

Clark Kimberling, Oct 12 2014

Keywords

• nonn
• easy

Comments

These are multinomial coefficients.

Examples

			a(2) = 6!/(1!*2!*3!) = 60.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000142, A001700, A248708, A248709, A248710.

Programs

Maple

seq(3*(3*n-1)!/((n-1)!^3*n*(n+1)), n=1..20); # Robert Israel, Mar 02 2017

Mathematica

Table[(3 n)!/((n - 1)! n! (n + 1)!), {n, 1, 20}]

PARI

a(n) = (3*n)! / ((n-1)!*n!*(n+1)!); \\ Amiram Eldar, Jun 11 2025

Sage

[3*factorial(3*n-1)/(factorial(n-1)^3*n*(n+1)) for n in range(1,19)] # Stefano Spezia, Aug 16 2024

Formula

a(n) ~ 3^(3*n+1/2) / (2*Pi*n). - Vaclav Kotesovec, Oct 19 2014

From Robert Israel, Mar 02 2017: (Start)

G.f.: 3*x*hypergeom([4/3, 5/3], [3], 27*x).

n*(n+2)*a(n+1) = 3*(3*n+1)(3*n+2)*a(n). (End)