How can I derive a bijection to show that the following equality holds?

$\displaystyle 2\displaystyle\sum\limits_{j=0}^{n-1} \binom{n-1+j}{j} = \binom{2n}{n}$

In class, we've been deriving bijections using lattice paths in-order to order to show that the size of both sets are the same. So for example, in class we've shown that the size of the set $\displaystyle L(a, b) = \binom{a+b}{b} $, where $\displaystyle L(a, b) $ is the set of lattice paths from (0, 0) to (a, b). Any suggestions?