Victor J. W. Guo: On a conjecture related to integer-valued polynomials, 449-453

Abstract:

Using the following $_4F_3$ transformation formula

$$\sum_{k=0}^{n}{-x-1\choose k}^2{x\choose n-k}^2=\sum_{k=0}^{n}{n+k\choose 2k}{2k\choose k}^2{x+k\choose 2k},$$

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.

Key Words: Zeilberger's algorithm, Chu-Vandermonde summation, integer-valued polynomials, multi-variable Schmidt polynomials.

2020 Mathematics Subject Classification: Primary 33C20; Secondary 11A07, 11B65, 05A10.

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