The Riordan Group

The group of Riordan arrays was introduced in 1991 by Shapiro, Getu, Woan, and Woodson [15], with the aim of defining a class of infinite lower triangular arrays with properties analogous to those of the Pascal triangle. A previous generalization of the Pascal, Catalan, and Motzkin triangles can be found in Rogers [13] who introduces the concept of renewal array. Sprugnoli [16, 17] also investigated these Riordan arrays and showed that they constitute a practical device for solving combinatorial sums by means of generating functions and the Lagrange inversion formula. Some of the structural properties of Riordan arrays were studied by Merlini, Rogers, Sprugnoli, and Verri [10]. Since then, these arrays attracted, and continue to attract, a lot of attention in the literature and many works on the Riordan arrays have been done, for example [3–6, 8, 12, 14, 18, 19].