A Combinatorial Interpretation of j/n*{kn}\choose{n+j}.
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.
