Identities between polynomials related to Stirling and harmonic numbers. (English) Zbl 1315.11018

Kellner, Bernd C.

Integers 14, Paper A54, 22 p. (2014).

The author investigates the polynomials \(\sum_{k=1}^n k!S(n,k)x^k\) and \(\sum_{k=1}^n k!S(n,k)H_kx^k\), where \(S(n,k)\) is the Stirling number of second kind and \(H_k\) is the harmonic number. He studies values, integrals and valuations related to these polynomials.

Reviewer: László A. Székely (Columbia)

MSC:

11B73	Bell and Stirling numbers
05A15	Exact enumeration problems, generating functions
11B83	Special sequences and polynomials
11B75	Other combinatorial number theory

Keywords:

Stirling numbers; Bernoulli numbers; Genocchi numbers; 2-adic valuation; harmonic numbers