On the properties of even and odd sequences

Abstract

In this paper we continue to investigate the properties of those sequences $\{a_n\}$ satisfying the condition ${\sum }_{k=0}^n\left(\genfrac{}{}{0ex}{}{n}{k}\right)(-1{)}^k{a}_k=\pm a_n$ $(n\ge 0)$. As applications we deduce new recurrence relations and congruences for Bernoulli and Euler numbers.

arXiv comment22 pages