Need help with this proof on balls and urns.

Recall that a lattice path on the grid from (0, 0) to (n, n) can be viewed as a sequence of length 2n which contains nmany R's and nrnany U's. Let (7\" be the number of such paths which never go above the diagonal, i.e., those sequences in which there are never more US than Rs in any initial segment. Show that C is equal to the number of ways of placing it unlabelled balls in n labelled urns so that for each h with 1 S k E am there are at most kInany balls total in the rst kInany urns