Stirling Behavior is Asymptotically Normal

Abstract

The Stirling numbers $\{\sigma_n^j\}$ of the second kind are asymptotically normal. This result is similar to results achieved by Feller [1] and Goncarov [2] for other combinatorial distributions. Here the technique of proof is different; one of the most general forms of the central limit theorem is used. Interesting qualitative information about the Stirling numbers is also obtained from this result. Asymptotic estimates on the value of $\max_j \{\sigma^j_n\}$ are given.