\[s\left(n,n-k\right)=\sum_{j=0}^{k}(-1)^{j}\genfrac{(}{)}{0.0pt}{}{n-1+j}{k+j}%
\,\genfrac{(}{)}{0.0pt}{}{n+k}{k-j}\*S\left(k+j,j\right),\]