A062030 Group even numbers into (2,4), (6,8,10,12), (14,16,18,20,22,24), ...; a(n) = product of n-th group.

8, 5760, 42577920, 1300252262400, 111644006842368000, 21695920874860629196800, 8291067715225260172247040000, 5644260808699395278689265516544000, 6360332664265371581768550654463180800000, 11209384544297234954537967755979151481241600000, 29531169256166572959626706182319305835700813824000000

Offset: 1

Author

Amarnath Murthy, Jun 02 2001

Keywords

• nonn

Comments

a(113) has 997 digits and a(114) has 1007 digits. - Harvey P. Dale, Nov 24 2024

Examples

			a(3) = 14*16*18*20*22*24 = 42577920.
		

Links

• Harry J. Smith, Table of n, a(n) for n=1..100

Crossrefs

Cf. A062029, A062031, A062032.

Programs

Mathematica

Table[4^n*Gamma[1+n+n^2]/Gamma[1-n+n^2], {n,30}] (* G. C. Greubel, May 05 2022 *)
Module[{nn=20,ev,l},ev=2*Range[nn(nn+1)];l=2*Range[nn];Times@@@TakeList[ev,l]] (* Harvey P. Dale, Nov 24 2024 *)

PARI

a(n) = { 2^(2*n)*(n^2+n)!/(n^2-n)! } \\ Harry J. Smith, Jul 30 2009

SageMath

[4^n*gamma(1+n+n^2)/gamma(1-n+n^2) for n in (1..30)] # G. C. Greubel, May 05 2022

Formula

a(n) = 4^n * Gamma(1 + n + n^2)/Gamma(1 - n + n^2). - G. C. Greubel, May 06 2022

a(n) ~ 4^n * n^(4*n). - Vaclav Kotesovec, Jun 09 2025

Extensions

More terms from Jason Earls, Jun 10 2001

Typo in a(4) corrected by N. J. A. Sloane, Aug 31 2009 using the b-file.