Abstract: The complete central Delannoy number can be defined by Delannoy triangle or counting of lattice path. By using A-matrix of Riordan matrix, the Riordan matrix expressions of several lattice paths are derived. Several combinatorial explanations of the complete central Delannoy numbers are given and the relationship between these matrices and the complete central Delannoy number is also considered.

Key words: Lattice path, Riordan matrix, A-matrix, the complete central Delannoy number