Limit Involving Some Permutations

[Leroy Quet]

I just submitted the following sequence:

>%S A000001 1,12,151200
>%N A000001 Number of permutations of {1,2,3,...,n^2} where no multiples of 
>n are consecutive.
>%C A000001 limit{n->oo} a(n)/(n^2)! = 1/e.
>%F A000001 (n^2 -n)! (n^2 -n +1)! /(n^2 -2n +1)!
>%e A000001 If n = 2, we have the permutations:
>1,2,3,4; 1,4,3,2; 3,2,1,4; 3,4,1,2;
>2,1,3,4; 4,1,3,2; 2,3,1,4; 4,3,1,2;
>2,1,4,3; 4,1,2,3; 2,3,4,1; 4,3,2,1
>(No multiples of 2 are adjacent in any of the permutations.)
>So a(2) = 12.
>%O A000001 1
>%K A000001 ,more,nonn,


First, I did not make a careless mistake and get the formula (in the 
%F-line) wrong, did I?

Second, is the limit in the %C-line correct?
It seems to follow directly from the formula in the %F-line, but I may 
have made a careless mistake in getting this limit.

thanks,
Leroy Quet