Riordan Arrays And The Generating Functions Of The Sequences

The Riordan array is an important tool for studying combinatorial sequences and identities. In this paper, we use the Riordan array to study some combinatorial sequences and identities. The main content of this thesis is listed as follows:In Chapter 1, we introduce the relative concepts of combinatorial sequences and identities, and research status of Riordan array theorems.In Chapter 2, we give a brief introduction of generating function, Lagrange inversion formula, Riordan array theorem and Riordan group. We also give the method to calculate the explicit expression of sequences in the Bell array and the associated array by using the Lagrange inversion formula and the Riordan array.In Chapter 3. we summarize the relative concepts and properties of Bell array, as-sociated array and Riordan array of the form (g(x), x2g(x)). We give the corresponding proofs of matrix identities. We also use the fundamental theorems in the second chapter to get the generating functions of the sequences in the Bell array and associated array.