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ON THE DIVISIBILITY OF SUMS INVOLVING APÉRY-LIKE POLYNOMIALS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 106 / Issue 2 / October 2022
- Published online by Cambridge University Press:
- 14 March 2022, pp. 203-208
- Print publication:
- October 2022
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- Article
- Export citation
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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.
