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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-15,
author = {Anna Dorota Krystek and \L ukasz Jan Wojakowski},
title = {Remarks on Catalan and super-Catalan numbers},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {237-244},
zbl = {1259.46055},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-15}
}
Anna Dorota Krystek; Łukasz Jan Wojakowski. Remarks on Catalan and super-Catalan numbers. Banach Center Publications, Tome 95 (2011) pp. 237-244. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-15/