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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..30
Programs
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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
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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