2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164736We define and study a series indexed by rooted trees and with coefficients in Q(q). We show that it is related to a family of Lie idempotents. We prove that this series is a q-deformation of a more classical series and that some of its coefficients are Carlitz q-Bernoulli numbers.19 pages, 2 figuresQuantum Algebra05C05, 17D25, 17Dtext