Touchard polynomial

English

Etymology

Studied by Template:W.

Noun

1. Template:Lb Any member of a polynomial sequence of binomial type defined by $T_n(x)=\sum _{k=0}^{n}S(n,k)x^k=\sum _{k=0}^n\left\{\genfrac{}{}{0ex}{}{n}{k}\right\}{x}^k,$ where $S(n,k)=\left\{\genfrac{}{}{0ex}{}{n}{k}\right\}$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.