Formula for the number of latin squares of size $n$? Is there a "easy to compute" formula for the number of Latin Squares or the number of reduced Latin squares of size $n$?--prophetes.ai

Formula for the number of latin squares of size $n$? Is there a "easy to compute" formula for the number of Latin Squares or the number of reduced Latin squares of size $n$?

No - if there was then OEIS A002860 and A000315 would have a formula: instead it labels the calculation as hard.

The numbers have been calculated up to $n=11$ in McKay, B. D. and Wanless, I. M. "On the Number of Latin Squares." _Ann. Combin._ 9, 335-344, 2005 which you can read (with subscription) at Springer or (without) at arXiv.