Here presented is a unified expression of Stirling numbers and their generalizations by using generalized factorial functions and generalized divided difference. Three algorithms for calculating the Stirling numbers and their generalizations based on our unified form are also given, which include a comprehensive algorithm using the characterization of Riordan arrays.
He, Tian-Xiao, "Expression and Computation of Generalized Stirling Numbers" (2013). Scholarship. 53.