Counting Deterministic Finite Automata

I have a question regarding counting DFAs:


Given a Σ = {0, 1} input string, with the state set Q = {1...n}, how would I find the total number of DFAs that can be constructed?

I believe this is a combinatorics problem, but I am not really sure what I would have to multiply.

Thanks.

This is indeed a nontrivial problem. A solution can be found in this paper: Enumeration and Random Generation of Accessible Automata.

StackExchange Computer Science Q#14778, answer score: 5