Identities and congruences for a new sequence

Mathematics – Number Theory

Scientific paper

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18 pages

Scientific paper

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

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