# Stirling numbers of the second kind

From specialfunctionswiki

The Stirling numbers of the second kind, commonly written as $S(n,k)$ or $\begin{Bmatrix}n \\ k\end{Bmatrix}$ are given by $$S(n,k)=\dfrac{1}{k!} \displaystyle\sum_{j=0}^{k} (-1)^{k-j} {k \choose j} j^n,$$ where ${k \choose j}$ denotes a binomial coefficient. The Stirling numbers of the second kind appear in the definition of the Bell numbers and Touchard polynomials.