The Eulerian numbers and a Pascal-like triangle

• Main Authors: Ang, Joel C., Aguilar, Maria Johanna C.
• Format: text
• Language: English
• Published: Animo Repository 1995
• Subjects: Euler's numbers; Pascal's triangle; Matrices; Sequences (Mathematics)
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16236
• Institution: De La Salle University

In this study, a number pattern similar to Pascal's triangle is presented. This number pattern referred to as the Pascal-like Triangle could be generated using three different methods. The first method generates the entries of the triangle by taking the weighted sum of its overhead entries. The second method generates the entries of the triangle by using a recurrence relation defined by the Eulerian Numbers. The third method generates the entries of the triangle by solving for the permanents of n x n circulant matrices. It shows also that the Eulerian numbers could be used in evaluating the series nm x n and in solving for the sum of the powers of the first n integers.