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Congruences for Catalan-Larcombe-French numbers | Xiao-Juan Ji
; Zhi-Hong Sun
; | Date: |
4 May 2015 | Abstract: | Let ${P_n}$ be the Catalan-Larcombe-French numbers given by $P_0=1, P_1=8$
and $n^2P_n=8(3n^2-3n+1)P_{n-1}-128(n-1)^2P_{n-2}$ $(nge 2)$, and let
$S_n=P_n/2^n$. In this paper we determine
$S_{np}-S_npmod{p^{3+ ext{ord}_pn}}$, where $p$ is an odd prime, $n$ is a
positive integer and $ ext{ord}_pn$ is the unique nonnegative integer $alpha$
such that $p^{alpha}mid n$ and $p^{alpha+1}
mid n$. We also determine
$S_{np+1}pmod{p^3}$. | Source: | arXiv, 1505.0668 | Services: | Forum | Review | PDF | Favorites |
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