The authors solve the following Jensen type functional equation
where and are nonnegative integers with . Moreover, they prove the stability of the above functional equation in the spirit of D.H. Hyers, G. Isac and Th.M. Rassias [Stability of functional equations in several variables. Progress in Nonlinear Differential Equations and their Applications. 34. Boston, MA: Birkhäuser (1998; Zbl 0907.39025)].