Stirling polynomials

Stirling polynomials are a family of polynomials related to Stirling numbers, which arise in combinatorics, particularly in the context of partitioning sets and distributions of objects. There are two main types of Stirling numbers: the "Stirling numbers of the first kind" \( S(n, k) \) and the "Stirling numbers of the second kind" \( \left\{ n \atop k \right\} \).