S ⁡ ( n , m ) = 1 m ! ⁢ ∑ k = 0 n − 1 ⟨ n k ⟩ ⁢ k n − m S\left(n,m\right)={\frac {1}{m!}}\sum _{k=0}^{n-1}\langle {\frac {n}{k}}\rangle {\frac {k}{n-m}}