Remarks on Catalan and super-Catalan numbers
Volume 96 / 2011
Banach Center Publications 96 (2011), 237-244
MSC: 46L53, 46L54, 60E10.
DOI: 10.4064/bc96-0-15
Abstract
In this article we discuss the Catalan and super-Catalan (or Schröder) numbers. We start with some combinatorial interpretations of those numbers. We study two probability measures in the context of free probability, one whose moments are super-Catalan, and another, whose even moments are super-Catalan and odd moments are zero. With the use of the latter we also show some new formulae for evaluation of the Catalans in terms of super-Catalans and vice-versa.
