Finding Euler number using box algebra and generalized skew-hooks (with computer program)

• Main Authors: Ang, Stanley A., Calayan, Emmanuel G.
• Format: text
• Language: English
• Published: Animo Repository 1994
• Subjects: Euler's numbers; Algebra > Computer programs; Programming (Mathematics); Skew fields; Linear operators > Generalized inverses; Fields, Algebraic
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16156
• Institution: De La Salle University

This paper discusses the recursive formula En+1= 1/2EiEn-i, with initial conditions Eo = 1, and E1 = 1, for finding the Euler numbers. These numbers appear as the coefficients of the Maclaurin series expansion for sec x and tan x.The main objective of this paper is to present a nonrecursive formula for obtaining the Euler numbers. This makes use of skew-hooks and column products. Euler numbers are expressed as linear combinations of multinomial coefficients. Also a computer program was developed to generate some of these Euler numbers.