  Catalan numbers $C(n)=\frac{1}{n+1}{2n\choose n}$ enumerate binary trees and
Dyck paths. The distribution of paths with respect to their number $k$ of
factors is given by ballot numbers $B(n,k)=\frac{n-k}{n+k}{n+k\choose n}$.
These integers are known to satisfy simple recurrence, which may be visualised
in a ``Catalan triangle'', a lower-triangular two-dimensional array. It is
surprising that the extension of this construction to 3 dimensions generates
integers $B_3(n,k,l)$ that give a 2-parameter distribution of $C_3(n)=\frac 1
{2n+1} {3n\choose n}$, which may be called order-3 Fuss-Catalan numbers, and
enumerate ternary trees. The aim of this paper is a study of these integers
$B_3(n,k,l)$. We obtain an explicit formula and a description in terms of trees
and paths. Finally, we extend our construction to $p$-dimensional arrays, and
in this case we obtain a $(p-1)$-parameter distribution of $C_p(n)=\frac 1
{(p-1)n+1} {pn\choose n}$, the number of $p$-ary trees.
