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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.
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%I #19 Aug 29 2024 05:26:52

%S 1,8,105,1920,45045,1290240,43648605,1703116800,75293843625,

%T 3719607091200,203067496256625,12140797545676800,788917222956988125,

%U 55362036808286208000,4172583192219510193125,336158287499913854976000

%N 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.

%H G. C. Greubel, <a href="/A113551/b113551.txt">Table of n, a(n) for n = 1..350</a>

%F a(n) = 2^n*Gamma(3*n/2)/Gamma(n/2). Column 2 of A303489. - _Peter Bala_, Jan 12 2020

%F a(n) ~ 3^((3*n-1)/2) * n^n / exp(n). - _Vaclav Kotesovec_, Aug 29 2024

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

%p seq(mul((2*k+n), k=1..n)/3, n=1..16); # _Zerinvary Lajos_, Jan 29 2008

%t Do[Print[Product[n + 2i, {i, 0, n - 1}]], {n, 1, 20}] (* Tracy Poff (tracy.poff(AT)gmail.com), Dec 31 2005 *)

%t 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 *)

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

%Y Cf. A113549, A113550, A303489.

%K easy,nonn

%O 1,2

%A _Amarnath Murthy_, Nov 03 2005

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