Congruences for sequences analogous to Euler numbers

Zhi-Hong Sun, Hai-Yan Wang

For a given real number $a$ we define the sequence $\{E_{n,a}\}$ by $E_{0,a}=1$ and $E_{n,a}=-a{\sum }_{k=1}^{[n/2]}\left(\genfrac{}{}{0ex}{}{n}{2k}\right)E_{n-2k,a}$ $(n\ge 1)$, where $[x]$ is the greatest in…