# How many distinct trees with N nodes?

I need help on this question regarding how many distinct trees exist given N nodes in the tree. "Distinct" here means that two isomorphic trees are counted as one. For 3 nodes, would the number of trees be 1 (since every other tree with 3 nodes is just an isomorphism of the other)?

Thanks.

I think the answer to your problem according to Cayley-Sylvester theorem is $n$ in the power of $n-2$.
• Also, this is wrong, because the $n^{n-2}$ formula distinguishes isomorphic trees with differently labeled vertices. – Misha Lavrov May 22 '17 at 16:46