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Permutations Related to Secant, Tangent and Eulerian Numbers

Published online by Cambridge University Press:  20 November 2018

Morton Abramson
Morton Abramson*
Affiliation:
Department of Mathematics, York University, 4700 Kelle Street, Downsview, Ont., M3J IP3
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It is well known that

1

where An denotes the number of "up-down" or alternating permutations

2

of 1, 2, …, n. The numbers A2n and A2n+1 are known as the secant and tangent numbers respectively and A2n = (—l)"E2n, where En is the Euler number.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 3 , 01 September 1979 , pp. 281 - 291
Copyright
Copyright © Canadian Mathematical Society 1979

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