William Y. C. Chen, Carol J. Wang, Larry X. W. Wang
Published 2007-08-20Version 1
We show that the limiting distributions of the coefficients of the $q$-Catalan numbers and the generalized $q$-Catalan numbers are normal. Despite the fact that these coefficients are not unimodal for small $n$, we conjecture that for sufficiently large $n$, the coefficients are unimodal and even log-concave except for a few terms of the head and tail.
Proof of a Conjecture of Chan, Robbins, and Yuen
Two New Identities Involving the Catalan Numbers: A classical approach
Chebyshev polynomials, their remarkable properties and connection with Catalan numbers
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