Generalized Schroder Matrices Arising from Enumeration of Lattice Paths

We introduce a new family of generalized Schroder matrices from the Riordan arrays which are obtained by counting of the weighted lattice paths with stepsE= (1, 0),D= (1, 1),N= (0, 1), andD ' = (1, 2) and not going above the liney=x. We also consider the half of the generalized Delannoy matrix which is derived from the enumeration of these lattice paths with no restrictions. Correlations between these matrices are considered. By way of illustration, we give several examples of Riordan arrays of combinatorial interest. In addition, we find some new interesting identities.