Generalizations of Modified Morgan-voyce Polynomials

In two recent articles [2] and [3], Ferri et al. introduced and studied the properties of two numerical triangles, which they called DFF and DFZ triangles. However, in a subsequent article, Andre-Jeannin [1] showed that the polynomials generated by the rows of these triangles are indeed the Morgan-Voyce polynomials Bn{x) and bn(x), whose properties are well known [10] and [11]; in fact, the polynomials Bn(x) and bn(x) have been used in the study of electrical networks since the 1960s (see, e.g., [8] and [9]). In the same article, Andre-Jeannin introduced a generalization of the Morgan-Voyce polynomials by defining the sequence of polynomials {i*(x)} by the relation Pf\x) = (x + 2)P$(x)-P&(xl {n>2\ (la) with P0(x) = l and Pl\x) = x+r + l. (lb)