Eulerian numbers

Abstract

The first interesting array of numbers a typical mathematics student encounters is Pascal’s triangle, shown in Table 1.1. It has many beautiful properties, some of which we will review shortly. One of the main points of this chapter is to argue that the array of Eulerian numbers is just as interesting as Pascal’s triangle.

Table 1.1 Pascal’s triangle of binomial coefficients $\binom{n}{k}$, 0 ≤ k ≤ n ≤ 9.