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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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