I have to get used to are, are notation and conventions. so how many bit strings are there of length N, well there's two to the N, so what's the OGF, it's two to the N, Z to the N, which is 2Z to the N, or one / one - 2Z, so that's another example of a combinatorial class. here's one familiar one recast in terms of analytic combinatorics. so the binary tree is empty or it's a noded two binary trees that's, that are in sequence in order that matters. so those are now familiar binary trees that we studied before. we know the counting sequence is the Catalan numbers. that was the subject of quite a bit of 