Remarkable relations between the central binomial series, Eulerian polynomials, and poly-Bernoulli numbers
Number Theory
2022-07-04 v1 Combinatorics
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.
Cite
@article{arxiv.2207.00205,
title = {Remarkable relations between the central binomial series, Eulerian polynomials, and poly-Bernoulli numbers},
author = {Beáta Bényi and Toshiki Matsusaka},
journal= {arXiv preprint arXiv:2207.00205},
year = {2022}
}
Comments
7 pages, to appear in Kyushu Journal of Mathematics, This article is an improvement of the second half of arXiv:2106.05585v1