\[S(n)=\tfrac{1}{2}n^{2}\ln n-\tfrac{1}{4}n^{2}+\tfrac{1}{2}n\ln n+\tfrac{1}{12}%
\ln n+C+\sum_{s=2}^{m-1}\frac{(-B_{2s})}{2s(2s-1)(2s-2)}\frac{1}{n^{2s-2}}+R_{%
m}(n),\]