A113551 a(n) = product of next n even numbers beginning with n if n is even, otherwise product of next n odd numbers beginning with n.

1, 8, 105, 1920, 45045, 1290240, 43648605, 1703116800, 75293843625, 3719607091200, 203067496256625, 12140797545676800, 788917222956988125, 55362036808286208000, 4172583192219510193125, 336158287499913854976000

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..350

Formula

a(n) = 2^n*Gamma(3*n/2)/Gamma(n/2). Column 2 of A303489. - Peter Bala, Jan 12 2020

a(n) ~ 3^((3*n-1)/2) * n^n / exp(n). - Vaclav Kotesovec, Aug 29 2024

Example

a(3) = 3*5*7 = 105, a(4) = 4*6*8*10 = 1920.

Maple

seq(mul((2*k+n), k=1..n)/3, n=1..16); # Zerinvary Lajos, Jan 29 2008

Mathematica

Do[Print[Product[n + 2i, {i, 0, n - 1}]], {n, 1, 20}] (* Tracy Poff (tracy.poff(AT)gmail.com), Dec 31 2005 *)
Table[Times@@Range[n, 3n-2, 2], {n, 20}] (* or *) Table[(2^n Gamma[(3n)/2])/Gamma[n/2], {n, 20}] (* Harvey P. Dale, Nov 28 2022 *)

Prog

(PARI) for(n=1, 25, print1(prod(k=0, n-1, n+2*k), ", ")) \\ G. C. Greubel, Sep 30 2017

Crossrefs

Cf. A113549, A113550, A303489.

Sequence in context: A001922 A264014 A222839 * A082735 A024358 A055406

Adjacent sequences: A113548 A113549 A113550 * A113552 A113553 A113554

Keyword

easy,nonn

Author

Amarnath Murthy, Nov 03 2005

Extensions

More terms from Tracy Poff (tracy.poff(AT)gmail.com), Dec 31 2005

Status

approved