Generalized Schröder permutations

We give the generating function for the integer sequence enumerating a class of pattern avoiding permutations depending on two parameters: image and image. The avoided patterns are the permutations of length image with the largest element in the first position and the second largest in one of the last image positions. For particular instances of image and image we obtain pattern avoiding classes enumerated by Schröder, Catalan and central binomial coefficient numbers, and thus, the obtained two-parameter generating function gathers under one roof known generating functions and expresses new ones. This work generalizes some earlier results of Barcucci et al. (2000) , Kremer (2000) and Kremer (2003) .