The author investigates the generalized Stirling numbers of the second kind introduced by L. C. Hsu and P. J.-S. Shiue [Adv. Appl. Math. 20, 366-384 (1998; Zbl 0913.05006)]. He derives for them horizontal and vertical recurrence relations, a formula for the ordinary generating function
(here should be probably replaced by ) and explicit formulae. In the end the evaluation
where , is proved.