I didn't immediately grasp what was being discussed, as I'm used to calling something else a skill tree — namely, the full set of possible progression paths for a specific generation. There are 255 such trees.
If we're evaluating the number of specific progression options up to, say, level 3, then by eye it seems to me there aren't 5, or 7, or 20, but significantly more, even accounting for choosing only "good" skills. I could be wrong — the eye is not a precise instrument.