Inequalities for binomial coefficients

Abstract

In this paper we prove several inequalities for binomial coefficients. For instance, if $k$ and $n$ are positive integers such that $n\ge 400$ and $[\frac{n}{5}]\le k\le [\frac{n}{2}]$, where $[x]$ is the greatest integer not exceeding $x$, then $$\binom nk<\Big(1-\frac{5(k-[\f n5])}{6n^2}\Big) \frac{n^{n-\f 12}}{k^k(n-k)^{n-k}}.$$

10 pages

References in corpus (1)

• On the properties of a sequence concerning binomial coefficients

Cited by in corpus (1)

• On the Combinatorics of Placing Balls into Ordered Bins