The Touchard polynomials, studied by Jacques Touchard, also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial type defined by T n = ∑ k = 0 n S x k = ∑ k = 0 n { n k } x k, {\displaystyle T_{n}=\sum _{k=0}^{n}Sx^{k}=\sum _{k=0}^{n}\left\{{n \atop k}\right\}x^{k},} where S = { n k } {\displaystyle S=\left\{{n \atop k}\right\}} is a Stirling number of the second kind, i.e., the number of partitions of a set of size n into k disjoint non-empty subsets. Wikipedia