Note on a new divisibility property of binomial sums

Abstract

The WZ method play an important role in proving combinatorial identities and congruences. In this paper, we use the WZ method to prove a new divisibility property on sums of binomial coefficients. For any integer n≥2, we have  n(2n n)∑_k=0^n-1(3k⁴/2k-1) (2k k)³ 16^n-k-1. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.