Remarkable relations between the central binomial series, Eulerian polynomials, and poly-Bernoulli numbers

2022/07/01 by Bényi, Beáta, Matsusaka, Toshiki
#05A05 #11B68 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2207.00205

Abstract

The central binomial series at negative integers are expressed as a linear combination of values of certain two polynomials. We show that one of the polynomials is a special value of the bivariate Eulerian polynomial and the other polynomial is related to the antidiagonal sum of poly-Bernoulli numbers. As an application, we prove Stephan's observation from 2004.

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