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
Examples
a(3) = 3*5*7 = 105, a(4) = 4*6*8*10 = 1920.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..350
Programs
-
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 *) -
PARI
for(n=1,25, print1(prod(k=0,n-1, n+2*k), ", ")) \\ G. C. Greubel, Sep 30 2017
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
Extensions
More terms from Tracy Poff (tracy.poff(AT)gmail.com), Dec 31 2005