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arxiv: 1203.5977 · v4 · pith:44O7CJVAnew · submitted 2012-03-27 · 🧮 math.NT · math.CO

On the further properties of \{U_n\}

classification 🧮 math.NT math.CO
keywords cdotcongruencesformulafunctionfurthergivengreatestinteger
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Let $\{U_n\}$ be given by $U_0=1$ and $U_n=-2\sum_{k=1}^{[n/2]} \b n{2k}U_{n-2k}\ (n\ge 1)$, where $[\cdot]$ is the greatest integer function. In the paper we present a summation formula and several congruences involving $\{U_n\}$.

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