$\displaystyle \prod_{i}^{n}(x_{1}+x_{2}+...+x_{i})$

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.