2004/01/22 by Ira M. Gessel, Guoce Xin, Gessel, Ira M. +1
Mathematics · #05A10 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A10
paper · pdf · doi:10.48550/arxiv.math/0401300
11 pages, 2 figures
arxiv created 2004/08/06 · arxiv updated 2009/12/01
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 \binom2nn, 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.