Summary: In this paper, we discuss the properties of associated Stirling numbers. By means of the method of coefficients, we establish a series of identities involving associated Stirling numbers, Bernoulli numbers, harmonic numbers, and the Cauchy numbers of the first kind. In addition, we give the asymptotic expansion of certain sums involving 2-associated Stirling numbers of the second kind by Darboux's method.

05A15, 05A16, 05A19

Stirling numbers, Bernoulli numbers, harmonic numbers, asymptotic expansion, Darboux's method