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arxiv: 1012.4034 · v1 · pith:3O4MERANnew · submitted 2010-12-17 · 🧮 math.NT

Identities and congruences for a new sequence

classification 🧮 math.NT
keywords congruencessequencebinomestablishexceedingformulasgivengreatest
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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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