Proof of Sun's conjecture on the divisibility of certain binomial sums

Abstract

In this paper, we prove the following result conjectured by Z.-W. Sun: $$(2n-1)\left(\genfrac{}{}{0ex}{}{3n}{n}\right)|\sum _{k=0}^n(\genfrac{}{}{0ex}{}{6k}{3k}\left)\right(\genfrac{}{}{0ex}{}{3k}{k}\left)\right(\genfrac{}{}{0ex}{}{6(n-k)}{3(n-k)}\left)\right(\genfrac{}{}{0ex}{}{3(n-k)}{n-k}).$$ by showing that the left-hand side divides each summand on the right-hand side.

5 pages

References in corpus (1)

• A q-rious positivity