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

0,1

Links

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

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A000178, A039622, A079402.

Sequence in context: A178981 A050923 A326960 * A270554 A037010 A294184

Adjacent sequences: A067697 A067698 A067699 * A067701 A067702 A067703

Keyword

nonn,easy

Author

Lekraj Beedassy, Feb 05 2002

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

Status

approved