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ON THE DIVISIBILITY OF SUMS INVOLVING APÉRY-LIKE POLYNOMIALS
Published online by Cambridge University Press: 14 March 2022
Abstract
We prove a divisibility result on sums involving the Apéry-like polynomials
$$ \begin{align*} V_n(x)=\sum_{k=0}^n {n\choose k}{n+k\choose k}{x\choose k}{x+k\choose k}, \end{align*} $$
which confirms a conjectural congruence of Z.-H. Sun. Our proof relies on some combinatorial identities and transformation formulae.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 106 , Issue 2 , October 2022 , pp. 203 - 208
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
The second author was supported by the National Natural Science Foundation of China (grant 12171370).
References
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