A071226 n-th power of the product of next n natural numbers.

1, 36, 1728000, 645241282560000, 6076911214672415134617600000, 3556852067865008593425339325122707718144000000, 269512166306728282203388439200933086924875888324090265600000000000000

Offset: 1

Author

Amarnath Murthy, May 17 2002

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..20

Crossrefs

Cf. A057003.

Programs

Maple

seq(product(n*(n-1)/2+i,i=1..n)^n,n=1..7);

Mathematica

Table[Pochhammer[1 + (n-1)*n/2, n]^n, {n, 1, 8}] (* Vaclav Kotesovec, Jul 13 2021 *)
With[{nn=10},(Times@@#)^Length[#]&/@TakeList[Range[(nn(nn+1))/2],Range[ nn]]] (* Harvey P. Dale, Aug 09 2021 *)

Formula

a(n) ~ exp(5/6) * n^(2*n^2) / 2^(n^2). - Vaclav Kotesovec, Jul 13 2021

Extensions

More terms from Sascha Kurz, Jan 02 2003