fixed Latin squares =? A000479(n)

[Alec Mihailovs]

> Let a(n) be A000479(n), the number of latin squares of order n with first 
> row 1,2,...,n; given by 1,1,1,2,24,1344,...
>
> Let b(n) be the number of fixed latin squares of order n, i.e., latin 
> squares of order n having all 1's on the diagonal.
>
> By direct enumeration, b(n) = a(n) for 1<=n<=5.
>
> Does b(n) = a(n) in general?

Yes. In both cases, all Latin squares of order n can be obtained by 
permutations of columns, so the number of all Latin squres of order n is the 
number of specified Latin squares multiplied by n! in both cases.

Alec Mihailovs