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\$\left\{ n \atop k \right\}\$ or \$S(n, k)\$ is a way of referring to the Stirling numbers of the second kind, the number of ways to partition a set of \$n\$ items into \$k\$ non-empty subsets. For example, to partition \$\{1,2,3,4\}\$ into \$2\$ non-empty subsets, we have
$$\begin{matrix}
\{\{1...