|Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.3|
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.
(Concerned with sequences A007054 and A007272 .)
Received March 5 2005; revised version received March 16 2005. Published in Journal of Integer Sequences April 27 2005.