The second production matrix of a Riordan array

TL;DR

This paper introduces the concept of the second production matrix of a Riordan array, explores its properties, and generalizes the idea to the n-th production matrix, expanding the theoretical framework of Riordan arrays.

Contribution

It defines and characterizes the second production matrix of a Riordan array and generalizes the concept to the n-th production matrix, advancing the theoretical understanding.

Findings

Characterization of the second production matrix.

Generalization to n-th production matrices.

Theoretical insights into Riordan array structures.

Abstract

A Riordan array is defined by its production matrix. In this paper, we explore the notion of the second production matrix of a Riordan array, characterizing the matrix that is generated by it. We indicate how this procedure can be generalized to the so-called $n$-th production matrix of a Riordan array.