A093434 a(n) = Product_{i=1..n} (2*n-i)*(2*n+i).

3, 180, 30240, 9979200, 5448643200, 4446092851200, 5068545850368000, 7694052600858624000, 15003402571674316800000, 36548288664598635724800000, 108767707065845539917004800000, 388300714225068577503707136000000

Offset

1,1

Comments

The arithmetic mean of these numbers is 2n.

The old definition was "a(n) = product of 2n distinct numbers, n just less than 2n and n just more than 2n."

Links

Robert Israel, Table of n, a(n) for n = 1..194

Formula

a(n) ~ 3^(3*n+1/2) * n^(2*n) / (2*exp(2*n)). - Vaclav Kotesovec, Oct 21 2014

From Robert Israel, Jan 16 2017: (Start)

a(n) = (3*n)!/(2*n!).

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

Example

a(3) = (3*4*5)*(7*8*9).

Maple

seq((3*n)!/(2*n!), n=1..50); # Robert Israel, Jan 16 2017

Mathematica

Table[(3n)!/(2n*(n - 1)!), {n, 12}] (* Robert G. Wilson v, Apr 24 2004 *)

Prog

(Magma) [Factorial(3*n)/(2*Factorial(n)): n in [1..15]]; // Vincenzo Librandi, Jan 17 2017
(PARI) for(n=1, 30, print1((3*n)!/(2*n!), ", ")) \\ G. C. Greubel, Feb 13 2018

Crossrefs

Sequence in context: A216967 A217443 A270245 * A053291 A013519 A042779

Adjacent sequences: A093431 A093432 A093433 * A093435 A093436 A093437

Keyword

nonn

Author

Amarnath Murthy, Apr 01 2004

Extensions

More terms from Robert G. Wilson v, Apr 24 2004

Replaced definition with formula provided by Vaclav Kotesovec, Oct 21 2014. - N. J. A. Sloane, Jan 17 2017

Status

approved