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pro vyhledávání: '"Larcombe, P."'
Autor:
Mukherjee, Sajal, Mukherjee, Sanjay
In this article, we have found significant generalization of the invariance properties of powers of matrices discovered by Larcombe, Fenessey and further explored by Zeilberger. Moreover, we found interesting new results exhibiting similar phenomena
Externí odkaz:
http://arxiv.org/abs/2109.10343
Akademický článek
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Autor:
Sun, Brian Yi, Wu, Baoyindureng
The Catalan-Larcombe-French sequence $\{P_n\}_{n\geq 0}$ arises in a series expansion of the complete elliptic integral of the first kind. It has been proved that the sequence is log-balanced. In the paper, by exploring a criterion due to Chen and Xi
Externí odkaz:
http://arxiv.org/abs/1602.04909
Autor:
Zhao, James J. Y.
Let $\{P_n\}_{n\geq 0}$ denote the Catalan-Larcombe-French sequence, which naturally came up from the series expansion of the complete elliptic integral of the first kind. In this paper, we prove the strict log-concavity of the sequence $\{\sqrt[n]{P
Externí odkaz:
http://arxiv.org/abs/1505.06650
Autor:
Mao, Guo-Shuai
Publikováno v:
Journal of Number Theory(2017)
The harmonic numbers $H_n=\sum_{0
Externí odkaz:
http://arxiv.org/abs/1511.06222
Autor:
Ji, Xiao-Juan, Sun, Zhi-Hong
Let $\{P_n\}$ be the Catalan-Larcombe-French numbers given by $P_0=1,\ P_1=8$ and $n^2P_n=8(3n^2-3n+1)P_{n-1}-128(n-1)^2P_{n-2}$ $(n\ge 2)$, and let $S_n=P_n/2^n$. In this paper we deduce congruences for $S_{mp^r}\pmod{p^{r+2}}$, $S_{mp^r-1}\pmod{p^r
Externí odkaz:
http://arxiv.org/abs/1505.00668
Autor:
Yang, Arthur L. B., Zhao, James J. Y.
We prove the log-concavity of the Fennessey-Larcombe-French sequence based on its three-term recurrence relation, which was recently conjectured by Zhao. The key ingredient of our approach is a sufficient condition for log-concavity of a sequence sub
Externí odkaz:
http://arxiv.org/abs/1503.02151
Autor:
Sun, Zhi-Hong
Let $\{f_n\}$ be the Franel numbers given by $f_n=\sum_{k=0}^n\binom nk^3$, and let $p>5$ be a prime. In this paper we mainly determine $\sum_{k=0}^{p-1} \binom{2k}k\frac{f_k}{m^k}\pmod p$ for $m=5,-16,16,32,-49,50,96$. Let $S_n=\sum_{k=0}^n\binom nk
Externí odkaz:
http://arxiv.org/abs/1502.02499
Akademický článek
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Autor:
Jarvis, Frazer, Verrill, Helena
We develop the Stienstra-Beukers theory of supercongruences in the setting of the Catalan-Larcombe-French sequence. We also give some applications to other sequences.
Comment: 14 pages: v2 has improved formatting
Comment: 14 pages: v2 has improved formatting
Externí odkaz:
http://arxiv.org/abs/0905.4187