A067700 a(n) = 2*(n^2)!*Product_{k=0..n-1} k!/(n+k)!.

2, 2, 4, 84, 48048, 1402298040, 3343286067469920, 950147368528779758457120, 44162749985403900797695349661715200, 440762756830149092247907829817237094171949712000

Offset: 0

Author

Lekraj Beedassy, Feb 05 2002

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..30

Crossrefs

Cf. A000178, A039622, A079402.

Programs

Magma

[n eq 0 select 2 else 2*Round(Factorial(n^2)*(&*[ Gamma(j+1)/Gamma(n+j+1): j in [0..n-1]])): n in [0..12]]; // G. C. Greubel, May 04 2021

Mathematica

Table[2*(n^2)!*BarnesG[n+1]^2/BarnesG[2n+1], {n, 0, 12}] (* G. C. Greubel, May 04 2021 *)

Sage

[2*factorial(n^2)*product( gamma(j+1)/gamma(n+j+1) for j in (0..n-1) ) for n in (0..12)] # G. C. Greubel, May 04 2021

Formula

(a(n)/2)^2 = A079402(n).

a(n) = 2*A039622(n). - Vaclav Kotesovec, Dec 17 2016

a(n) = 2*(n^2)!*BarnesG(n+1)^2/BarnesG(2*n+1), where BarnesG(n) = A000178(n). - G. C. Greubel, May 04 2021

Extensions

The original definition was unclear (at least to me) and the explicit formula provided did not match the sequence. The new definition was provided by Robert G. Wilson v and is a close match to the beginning of the old version. - N. J. A. Sloane, Feb 10 2002

Edited by Dean Hickerson, Jan 06 2003