On some divisibility properties of binomial sums

Abstract

In this paper, we consider two particular binomial sums 4 4k 2k 65536 n−k−1 , which are inspired by two series for 1 π 2 obtained by Guillera. We consider their divisibility properties and prove that they are divisible by 2n 2 2n n 2 for all integer n ≥ 2. These divisibility properties are stronger than those divisibility results found by He, who proved the above two sums are divisible by 2n 2n n with the WZ-method.