Can I list Stirling sets of the second kind of set of n elements?

Questions
1

Dear members of the community

Mathematica has a function to compute the Stirling number of the second kind StirlingS2[N] which is the cardinality of an Stirling set of the second kind. However, I have been looking for a Mathematica function to list those Stirling sets without success. Does anyone know if there exist such a direct function?

Regards

Jesus Rico

2

In[28]:= Table[StirlingS2[10, m], {m, 10}]

Out[28]= {1, 511, 9330, 34105, 42525, 22827, 5880, 750, 45, 1}