“…The infinite triangles of Pascal, Catalan, Motzkin and Schröder are important and meaningful examples of pRa's, and many others have been proposed and developed (see, e.g., [10,18,20]). In the recent literature, Riordan arrays have attracted the attention of various authors from many point of view and many examples and applications can be found (see, e.g., [1,6,11,[13][14][15]17,24,21] but the literature is still developing now). In particular, Merlini and Verri [15] pointed out an important connection between pRa's and generating trees and they call proper generating trees the corresponding trees.…”