The 2-adic valuations of Stirling numbers of the second kind

Shaofang Hong, Jianrong Zhao, Wei Zhao

In this paper, we investigate the 2-adic valuations of the Stirling numbers $S(n,k)$ of the second kind. We show that $v_2(S(4i,5))=v_2(S(4i+3,5))$ if and only if $i\not\equiv 7…