The Limiting Distribution of the Coefficients of the q-Catalan Numbers
William Y. C. Chen, Carol J. Wang, and Larry X.W. Wang
Abstract: 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.
AMS Classification: 05A16, 60C05
Keywords: Bernoulli number, q-Catalan number, unimodality, log-concavity, moment generating function.