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SOME PROPERTIES OF A SEQUENCE ANALOGOUS TO EULER NUMBERS
Published online by Cambridge University Press: 12 June 2012
Abstract
Let $\{U_n\}$ be given by $U_0=1$ and $U_n=-2\sum _{k=1}^{[n/2]} \binom n{2k}U_{n-2k}\ (n\ge 1)$, where $[\cdot ]$ is the greatest integer function. Then $\{U_n\}$ is analogous to the Euler numbers and $U_{2n}=3^{2n}E_{2n}(\frac 13)$, where $E_m(x)$ is the Euler polynomial. In a previous paper we gave many properties of $\{U_n\}$. In this paper we present a summation formula and several congruences involving $\{U_n\}$.
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- Research Article
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- Copyright © 2012 Australian Mathematical Publishing Association Inc.
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