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

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