  We introduce a multivariate generalization of normalized Chebyshev
polynomials of the second kind. We prove that these polynomials arise in the
context of cluster characters associated to Dynkin quivers of type $\mathbb A$
and representation-infinite quivers. This allows to obtain a simple
combinatorial description of cluster algebras of type $\mathbb A$. We also
provide explicit multiplication formulas for cluster characters associated to
regular modules over the path algebra of any representation-infinite quiver.
