Résumé | We define a sequence of polynomials associated with Motzkin paths and explore their properties. In particular we show that such polynomials satisfy a recurrence relation and present a remarkable symmetry.
We study in detail many different specializations of these polynomials that turn out to be sequences of great interest in combinatorics, such as Schroeder numbers, Fibonacci numbers, q-Catalan polynomials, Narayana polynomials. |