×

A note on degenerate Stirling numbers of the first kind. (English) Zbl 1439.11073

Summary: Recently, the degenerate Stirling numbers of the first kind were introduced. In this paper, we give some formulas for the degenerate Stirling numbers of the first kind in the terms of the complete Bell polynomials with higher-order harmonic number arguments. Also, we derive an identity connecting the degenerate Stirling numbers of the first kind and the degenerate derangement numbers by using probabilistic method.

MSC:

11B73 Bell and Stirling numbers
11B83 Special sequences and polynomials
05A19 Combinatorial identities, bijective combinatorics
PDFBibTeX XMLCite
Full Text: arXiv