a too-short sequence related to Latin squares

[Paul D Hanna]

Perhaps an interesting variation of this theme 
would be the number of such n X n squares 
with non-zero determinant? 
 
Paul

-- "N. J. A. Sloane" <njas at research.att.com> wrote:
Dear Seqfans,  is the following sequence already
in the OEIS?  one more term would be helpful!
Neil

How many n X n squares are there, filled with
the numbers 1...n, such that in row or column k,
for all k = 1...n, the number k appears at least once?

For n = 1 there is just 1,

for n = 2 there seem to be 6
namely

11 11 12 12 12 21
12 22 12 21 22 12