On the properties of a sequence concerning binomial coefficients

Daeyeoul Kim, Ayyadurai Sankaranarayanan, Zhi-Hong Sun

For $n\ge 3$ let $f(n)$ be the least positive integer $k$ such that $\left(\genfrac{}{}{0ex}{}{n}{k}\right)>\frac{2^n}{n+1}$. In this paper we investigate the properties of $f(n)$.