I need to prove the number of distinct monomials appearing in the expansion is the nth catalan number.

I tried to do induction, I don't believe it works. I need to do a bijection. I tried a lattic path which of course is a bijection because

it's also counted by a Catalan number, but proving it is a little hard.

http://i220.photobucket.com/albums/d...sc0054cf40.jpg