  The Super-Catalan numbers are a generalization of the Catalan numbers defined
as $T(m,n) = \frac{(2m)!(2n)!}{2m!n!(m+n)!}$. It is an open problem to find a
combinatorial interpretation for $T(m,n)$. We resolve this for $m=3,4$ using a
common form; no such solution exists for $m=5$.
