Schroder Matrix as Inverse of Delannoy Matrix

Using Riordan arrays, we introduce a generalized Delannoy matrix by weighted Delannoy numbers. It turn out that Delannoy matrix, Pascal matrix, and Fibonaccimatrix are all special cases of the generalized Delannoy matrices, meanwhile Schroder matrix and Catalan matrix also arise in involving inverses of the generalized Delannoy matrices. These connections are the focus of our paper. The half of generalized Delannoy matrix is also considered. In addition, we obtain a combinatorial interpretation for the generalized Fibonacci numbers.