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: 

  Keywords:  Bernoulli number, q-Catalan number, unimodality, log-concavity, moment generating function.

  Download:   PDF