Report Number: CS-TR-82-949
Institution: Stanford University, Department of Computer Science
Title: The r-Stirling numbers
Author: Broder, Andrei Z .
Date: December 1982
Abstract: The r-Stirling numbers of the first and second kind count restricted permutations and respectively restricted partitions, the restriction being that the first r elements must be in distinct cycles and respectively distinct subsets. The combinatorial and algebraic properties of these numbers, which is most cases generalize similar properties of the regular Stirling numbers, are explored starting from the above definition.
http://i.stanford.edu/pub/cstr/reports/cs/tr/82/949/CS-TR-82-949.pdf