How many trees can be drawn using$n$ vertices without rebuilding isomorphs?

Question

I'm told to draw all possible trees with exactly $6$ vertices. I was able to draw a maximum of $6$ trees. Any more were isomorphs of these $6$ trees.
How can I determine if I have drawn all the trees? For such a small number of vertex, I can try all variations but how to do the same for a large number of vertices? Is there any standard formula to counter-check?

Answer 1

See sequence A000055 in OEIS for number of trees with $n$ unlabeled nodes (up to isomorphism). As far as I'm aware, no closed formula is known.