Abstract
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 C(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.