A000519

[Brendan McKay]

* Brendan McKay <bdm at cs.anu.edu.au> [030419 23:01]:
> * Jim Nastos <nastos at cs.ualberta.ca> [030419 07:03]:
> > 
> >   If I can divert from this question for a moment...
> > There are a few sequences numbering the equivalence classes of latin 
> > squares for various definitions of equivalence... How come there is no 
> > sequence for the number latin squares up to isomorphism, where an 
> > isomorphism here is just any permutation of labels.
> 
> Right, that type of equivalence has been mentioned in the literature
> but I never saw any counts for it.
 
On second thoughts, it is the number of Latin squares for which
the first row is 1,2,3,...,n.  This is 1/n! times the total number
of squares, or (n-1)! times the number of reduced squares.

I guess it should be added to OEIS.  However, I don't see the connection
to isomorphism classes of transversal designs TD(3,n).  It seems to
me that the most natural definition of isomorphism for TDs is the
same as isotopy for Latin squares.

Brendan.