A062029 Group even numbers into (2), (4,6), (8,10,12), (14,16,18,20), ...; a(n) = product of n-th group.

2, 24, 960, 80640, 11531520, 2500485120, 763847884800, 312344808652800, 164644289755545600, 108684799028822016000, 87805845811395506995200, 85211145316323008446464000, 97803969545162680178835456000, 131047222390590123375392194560000, 202702319752278628965061257854976000

Offset: 1

Author

Amarnath Murthy, Jun 02 2001

Keywords

• nonn

Examples

			a(3) = 8*10*12 = 960.
		

Links

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

Crossrefs

Cf. A057003, A062030, A062031, A062032.

Programs

Mathematica

Table[2^n*Gamma[(2+n+n^2)/2]/Gamma[(2-n+n^2)/2], {n,30}] (* G. C. Greubel, May 05 2022 *)
With[{nn=30},Times@@@TakeList[Range[2,(nn(nn+1))/2,2],Range[nn/2]]] (* Harvey P. Dale, May 09 2022 *)

PARI

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

SageMath

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

Formula

a(n) = Product_{k=1..n} (n^2 - n + 2*k) = (n^2 + n)!!/(n^2 - n)!! .

a(n) = 2^n*Gamma((n^2 + n + 2)/2)/Gamma((n^2 - n + 2)/2).

a(n) = 2^n * A057003(n-1).

Extensions

Formula and more terms from Vladeta Jovovic, Jun 05 2001