2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97502We consider an integral series f(X,t) which depends on the choice of a set X of labelled planar rooted trees. We prove that its inverse for composition is of the form f(Z,t) for another set Z of trees, deduced from X. The proof is self-contained, though inspired by the Koszul duality theory of quadratic operads.Minor modifications and reference to further workCombinatoricsAlgebraic Topology05A15; 13F25; 18D50text