Super-Catalan Numbers of the Third and Fourth Kind

Abstract

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 $m=5$.

13 pages, no figures

References in corpus (1)

• A Combinatorial Interpretation of The Numbers $6(2n)!/n!(n+2)!$