Modular periodicity of the Euler up/down numbers at odd prime powers

Berke Güleç

Let $E_n$ denote the number of alternating permutations of $\{1,\dots ,n\}$, equivalently characterized by ${\sum }_{n\ge 0}{E}_n{z}^n/n!=\sec z+\tan z$. For every $q\ge 1$, the sequence $(E…