Journal of Integer Sequences, Vol. 17 (2014), Article 14.10.7

A Weighted Interpretation for the Super Catalan Numbers

Emily Allen and Irina Gheorghiciuc
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213


The super Catalan numbers T(m,n)=(2m)!(2n)!/2m!n!(m+n)! are integers that generalize the Catalan numbers. With the exception of a few values of m, no combinatorial interpretation is known for T(m,n). We give a weighted interpretation for T(m,n) and develop a technique that converts this weighted interpretation into a conventional combinatorial interpretation in the case m = 2.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000108 A007054 A007272.)

Received August 26 2014; revised version received August 31 2014; September 11 2014. Published in Journal of Integer Sequences, November 5 2014.

Return to Journal of Integer Sequences home page