An Empirical Method for Solving (rigorously!) Algebraic Functional   Equations Of the Form F(P(x,t), P(x,1),x,t)=0
  We present an empirical-yet-rigorous approach for solving a wide class of functional equations, thereby automating many results that previously required considerable human ingenuity and human labor. 
Ira M. Gessel and Doron Zeilberger
math.CO