Divisibility by 2 of Stirling numbers of the second kind and their differences

Jianrong Zhao, Shaofang Hong, Wei Zhao

Let $n,k,a$ and $c$ be positive integers and $b$ be a nonnegative integer. Let ${\nu }_2(k)$ and $s_2(k)$ be the 2-adic valuation of $k$ and the sum of binary digits of $k$, respectivel…