Some Inverse Relations Determined by Catalan Matrices

Abstract

We use the A-sequence and Z-sequence of Riordan array to characterize the inverse relation associated with the Riordan array. We apply this result to prove some combinatorial identities involving Catalan matrices and binomial coefficients. Some matrix identities obtained by Shapiro and Radoux are all special cases of our identity. In addition, a unified form of Catalan matrices is introduced.

On One-Parameter Catalan Arrays

“…We elaborate, in particular, on the product matrix C(r) = CP (r). Clearly, we have C( 0 Recently, Yang [23] introduced a generalized Catalan matrix, given by of degree n monomials in r, whose coefficients are polynomials in a and b, that have rational coefficients. The one-parameter Catalan triangles that we will study are instead given by…”