2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136314We 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.13 pagesCombinatoricstext