A062032 Group odd numbers into (1), (3,5), (7,9,11), (13,15,17,19), ...; a(n) = product of n-th group.

1, 15, 693, 62985, 9454725, 2118331215, 662496582825, 275735605996305, 147364622598587625, 98358760729571316975, 80185770642041047108125, 78405694972326706112753625, 90569612902695107431619494125, 122020670469540010360975931523375, 189638875693941730653122520269900625

Offset: 1

Author

Amarnath Murthy, Jun 02 2001

Keywords

• nonn

Examples

			a(3) = 7*9*11 = 693.
		

Links

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

Crossrefs

Cf. A062029, A062030, A062031.

Programs

Mathematica

len=20; Times@@@FoldPairList[TakeDrop,Range[1,len^2+len-1,2],Range[len]] (* The program uses the FoldPairList and TakeDrop functions from Mathematica version 10 *) (* Harvey P. Dale, Jul 29 2015 *)
Table[(Gamma[2*Binomial[n+1,2] +1]*Gamma[Binomial[n,2] +1])/(2^n*Gamma[Binomial[n +1,2] +1]*Gamma[2*Binomial[n,2] +1]), {n, 30}] (* G. C. Greubel, May 06 2022 *)

PARI

{ for (n=1, 100, b=n^2 - n + 1; write("b062032.txt", n, " ", prod(k=0, n - 1, b + 2*k)) ) } \\ Harry J. Smith, Jul 30 2009

SageMath

[(gamma(2*binomial(n+1,2) +1)*gamma(binomial(n,2) +1))/(2^n*gamma(binomial(n+1,2) +1)*gamma(2*binomial(n,2) +1)) for n in (1..30)] # G. C. Greubel, May 06 2022

Formula

a(n) = Product_{k=0..n-1} (2*k + n*(n-1) + 1). - Harry J. Smith, Jul 30 2009

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

a(n) ~ n^(2*n). - Vaclav Kotesovec, Jun 09 2025

Extensions

More terms from Jason Earls, Jun 08 2001