Riordan array

A Riordan array is an infinite lower triangular matrix, ${\displaystyle D}$, constructed out of two formal power series, ${\displaystyle d(t)}$ and ${\displaystyle h(t)}$, in such a way that ${\displaystyle d_{n,k}=[t^{n}]d(t)\left(th(t)\right)^{k}}$. A Riordan array is an element of the Riordan group.[1] It was created by mathematician Louis W. Shapiro.[1]

The study of Riordan arrays is a growing field that is both being influenced by, and continuing its contributions to, other fields such as combinatorics, group theory, matrix theory, number theory, probability, sequences and series, Lie groups and Lie algebras, orthogonal polynomials, graph theory, networks, Beal conjecture, Riemann hypothesis, unimodal sequences, combinatorial identities, elliptic curves, numerical approximation, asymptotics, and data analysis. Riordan arrays is also a powerful unifying concept, binding together important tools: generating functions, computer algebra systems, formal languages, path model, and so on.[2]