On the r-Shifted Central Coefficients of Riordan Matrices

By presenting Riordan matrix as a triangle, the central coefficients are entries in the central column. Starting at the central column, the r-shifted central coefficients are entries in column r of the right part of the triangle. This paper aims to characterize the r-shifted central coefficients of Riordan matrices. Here we will concentrate on four elements of the subgroups of the Riordan group, that is, the Bell subgroup, the associated subgroup, the derivative subgroup, and the hitting time subgroup. Some examples are presented to show how we deduce the generating functions for interesting sequences by using different means of calculating these r-shifted central coefficients. Besides, we make some extensions in the Bell subgroup.