Identities and congruences for a new sequence

Abstract

Let $[x]$ be the greatest integer not exceeding $x$. In the paper we introduce the sequence $\{U_n\}$ given by $U_0=1$ and $U_n=-2{\sum }_{k=1}^{[n/2]}\left(\genfrac{}{}{0ex}{}{n}{2k}\right)U_{n-2k}(n\ge 1)$, and establish many recursive formulas and congruences involving $\{U_n\}$.

18 pages