I know the combinatorial interpretation of first, and second order Stirling numbers (#of k cycles of n items, and #of partitions n items into k subsets). Is there an interpretation for the generalized Stirling numbers?



Combinatorial Interpretation of Generalized Stirling numbers
[Combinatorial Interpretation of Generalized Stirling Numbers](https://cs.uwaterloo.ca/journals/JIS/VOL12/Lang/lang.pdf) (2009)



> 
> A combinatorial interpretation of the earlier studied generalized
>  Stirling numbers, emerging in a normal ordering problem and its
>  inversion, is given. It involves unordered forests of certain types of
>  labeled trees. Partition number arrays related to such forests are
>  also presented.
> 
> 
> 


