  It is well known that the numbers $(2m)! (2n)!/m! n! (m+n)!$ are integers,
but in general there is no known combinatorial interpretation for them. When
$m=0$ these numbers are the middle binomial coefficients $\binom{2n}{n}$, and
when $m=1$ they are twice the Catalan numbers. In this paper, we give
combinatorial interpretations for these numbers when $m=2$ or 3.
