An extension of Gauss congruences for Apéry numbers
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913329244536832 |
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| author | Liu, Ji-Cai |
| author_facet | Liu, Ji-Cai |
| contents | Osburn, Sahu and Straub introduced the numbers: \begin{align*} A_n^{(r,s,t)}=\sum_{k=0}^n{n\choose k}^r{n+k\choose k}^s{2k\choose n}^t, \end{align*} for non-negative integers $n,r,s,t$ with $r\ge 2$, which includes two kinds of Apéry numbers and four kinds of Apéry-like numbers as special cases, and showed that the numbers $\{A_n^{(r,s,t)}\}_{n\ge 0}$ satisfy the Gauss congruences of order $3$. We establish an extension of Osburn--Sahu--Straub congruence through Bernoulli numbers, which is one step deep congruence of the Gauss congruence for $A_n^{(r,s,t)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16636 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An extension of Gauss congruences for Apéry numbers Liu, Ji-Cai Number Theory Combinatorics 11B50, 11B65, 11B68 Osburn, Sahu and Straub introduced the numbers: \begin{align*} A_n^{(r,s,t)}=\sum_{k=0}^n{n\choose k}^r{n+k\choose k}^s{2k\choose n}^t, \end{align*} for non-negative integers $n,r,s,t$ with $r\ge 2$, which includes two kinds of Apéry numbers and four kinds of Apéry-like numbers as special cases, and showed that the numbers $\{A_n^{(r,s,t)}\}_{n\ge 0}$ satisfy the Gauss congruences of order $3$. We establish an extension of Osburn--Sahu--Straub congruence through Bernoulli numbers, which is one step deep congruence of the Gauss congruence for $A_n^{(r,s,t)}$. |
| title | An extension of Gauss congruences for Apéry numbers |
| topic | Number Theory Combinatorics 11B50, 11B65, 11B68 |
| url | https://arxiv.org/abs/2404.16636 |