Touchard polynomial

(mathematics) Any member of a polynomial sequence of binomial type defined by T_n(x)=∑ₖ₌₀ⁿS(n,k)xᵏ=∑ₖ₌₀ⁿn atop kxᵏ, where S(n,k)=n atop kis 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.