A248708 a(n) = f(4*n+2)/(f(n-1)*f(n)*f(n+1)*f(n+2)), where f(k) = k!.

60, 12600, 2522520, 514594080, 107550162720, 22969641895200, 4995897112206000, 1103284402265073600, 246784661070292144800, 55803246694136969227200, 12736017918577260592084800, 2930174751896446667689440000, 678879630375093886522676256000, 158257286142440155623613107216000

Offset: 1

Author

Clark Kimberling, Oct 12 2014

Keywords

• nonn
• easy

Comments

These are multinomial coefficients.

Examples

			a(2) = 10!/(1!*2!*3!*4!) = 12600.
		

Links

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

Crossrefs

Cf. A000142, A001700, A248707, A248709, A248710.

Programs

Mathematica

Table[(4 n + 2)!/((n - 1)! n! (n + 1)! (n + 2)!), {n, 1, 20}]

Sage

[factorial(4*n + 2)/(factorial(n - 1)* factorial(n)*factorial(n + 1)*factorial(n + 2)) for n in range(1,14)] # Stefano Spezia, Aug 16 2024

Formula

a(n) ~ 2^(8*n+7/2) / (Pi^(3/2) * n^(3/2)). - Vaclav Kotesovec, Oct 19 2014