  We consider a generalization of Eulerian numbers which count the number of
placements of $cn$ "rooks" on an $n\times n$ board where there are exactly $c$
rooks in each row and each column, and exactly $k$ rooks below the main
diagonal. The standard Eulerian numbers correspond to the case $c=1$. We show
that for any $c$ the resulting numbers are symmetric and give generating
functions of these numbers for small values of $k$.
