  We define a new family of generalized Stirling permutations that can be
interpreted in terms of ordered trees and forests. We prove that the number of
generalized Stirling permutations with a fixed number of ascents is given by a
natural three-parameter generalization of the well-known Eulerian numbers. We
give the generating function for this new class of numbers and, in the simplest
cases, we find closed formulas for them and the corresponding row polynomials.
By using a non-trivial involution our generalized Eulerian numbers can be
mapped onto a family of generalized Ward numbers, forming a Riordan inverse
pair, for which we also provide a combinatorial interpretation.
