  The identity j/n {kn}\choose{n+j} =(k-1) {kn-1}\choose{n+j-1}-
{kn-1}\choose{n+j} shows that j/n {kn}\choose{n+j} is always an integer. Here
we give a combinatorial interpretation of this integer in terms of lattice
paths, using a uniformly distributed statistic. In particular, the case j=1,k=2
gives yet another manifestation of the Catalan numbers.
