Riordan arrays and their applications

The concept of a Riordan array is used in a constructive way to find the generating function of many combinatorial sums. The generating function can then help us to obtain the closed form of the sum or its asymptotic value. Some examples of sums involving binomial coefficients and Stirling numbers are examined together with some applications of Riordan arrays to combinatorial sum inversion, walk problem, B-trees and asymptotics for convolution matrices.