Tags: #definition

Eulerian triangle

The Eulerian triangle is the triangle with entries in the $n$th row the coefficients of the $n$th Eulerian polynomial:

Properties

• Each row $n$ sums to $n!$
• It is given by the relation $a_{n,i}=i{a}_{n-1,i}+(n-i)a_{n-1,i-1}$
  • For the proof, see Eulerian numbers are coefficients of Eulerian polynomial