cp's OEIS Frontend

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.

%I A113551 #19 Aug 29 2024 05:26:52
%S A113551 1,8,105,1920,45045,1290240,43648605,1703116800,75293843625,
%T A113551 3719607091200,203067496256625,12140797545676800,788917222956988125,
%U A113551 55362036808286208000,4172583192219510193125,336158287499913854976000
%N 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.
%H A113551 G. C. Greubel, <a href="/A113551/b113551.txt">Table of n, a(n) for n = 1..350</a>
%F A113551 a(n) = 2^n*Gamma(3*n/2)/Gamma(n/2). Column 2 of A303489. - _Peter Bala_, Jan 12 2020
%F A113551 a(n) ~ 3^((3*n-1)/2) * n^n / exp(n). - _Vaclav Kotesovec_, Aug 29 2024
%e A113551 a(3) = 3*5*7 = 105, a(4) = 4*6*8*10 = 1920.
%p A113551 seq(mul((2*k+n), k=1..n)/3, n=1..16); # _Zerinvary Lajos_, Jan 29 2008
%t A113551 Do[Print[Product[n + 2i, {i, 0, n - 1}]], {n, 1, 20}] (* Tracy Poff (tracy.poff(AT)gmail.com), Dec 31 2005 *)
%t A113551 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 A113551 (PARI) for(n=1,25, print1(prod(k=0,n-1, n+2*k), ", ")) \\ _G. C. Greubel_, Sep 30 2017
%Y A113551 Cf. A113549, A113550, A303489.
%K A113551 easy,nonn
%O A113551 1,2
%A A113551 _Amarnath Murthy_, Nov 03 2005
%E A113551 More terms from Tracy Poff (tracy.poff(AT)gmail.com), Dec 31 2005