A combinatorial generalization of the Stirling Numbers of the second kind

A combinatorial generalization of the Stirling Numbers of the second kind is presented as the number of partitions of a set with n elements in m subsets with at least c elements each. An equivalence with a previous definition is discussed. Combinatorial properties and a recursive relation are obtained. The generating function is obtained as the m-th power of a truncated exponential series expansion at c. Other applications are also discussed.