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

Offset

1,2

Links

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

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

Example

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

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A062029, A062030, A062031.

Sequence in context: A209499 A001520 A062079 * A204251 A281764 A209740

Adjacent sequences: A062029 A062030 A062031 * A062033 A062034 A062035

Keyword

nonn

Author

Amarnath Murthy, Jun 02 2001

Extensions

More terms from Jason Earls, Jun 08 2001

Status

approved