ON THE DIVISIBILITY OF SUMS INVOLVING APÉRY-LIKE POLYNOMIALS

Abstract

AbstractWe 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.