On a conjecture related to integer-valued polynomials

Abstract

Using the following ${}_4{F}_3$ transformation formula $$\sum _{k=0}^n{\left(\genfrac{}{}{0ex}{}{-x-1}{k}\right)}^2{\left(\genfrac{}{}{0ex}{}{x}{n-k}\right)}^2=\sum _{k=0}^n\left(\genfrac{}{}{0ex}{}{n+k}{2k}\right){\left(\genfrac{}{}{0ex}{}{2k}{k}\right)}^2\left(\genfrac{}{}{0ex}{}{x+k}{2k}\right),$$ which can be proved by Zeilberger's algorithm, we confirm some special cases of a recent conjecture of Z.-W. Sun on integer-valued polynomials.

5 pages

References in corpus (1)

• Some new $q$-congruences for truncated basic hypergeometric series: even powers