\displaystyle {\frac {291}{400}}+\sum _{\alpha={\rm RootOf} \left( {{\rm \_Z}}^{5}+2 \,{{\rm \_Z}}^{4}+2\,{{\rm \_Z}}^{3}+2\,{{\rm \_Z}}^{2}+2\,{\rm \_Z}+1 \right) }{\frac {1}{2000}}\, \left( 1+\alpha+17\,{\alpha}^{2}+9\,{ \alpha}^{3}+17\,{\alpha}^{4} \right) {\alpha}^{-2-n} \left( n+1 \right) +\sum _{\alpha={\rm RootOf} \left( {{\rm \_Z}}^{5}+2\,{{\rm \_Z}}^{4}+2\,{{\rm \_Z}}^{3}+2\,{{\rm \_Z}}^{2}+2\,{\rm \_Z}+1 \right) }-{\frac {1}{500}}\, \left( 3-33\,\alpha-14\,{\alpha}^{2}-27\,{\alpha}^ {3}+{\alpha}^{4} \right) {\alpha}^{-1-n}+\sum _{\alpha={\rm RootOf} \left( {{\rm \_Z}}^{4}-{{\rm \_Z}}^{3}+{{\rm \_Z}}^{2}-{\rm \_Z}+1 \right) }{\frac {1}{100}}\, \left( 2\,\alpha+4\,{\alpha}^{3}-3\,{ \alpha}^{2}-6 \right) {\alpha}^{-1-n}+{\frac {9}{200}}\,{n}^{2}+{\frac {421}{1200}}\,n+{\frac {1}{600}}\,{n}^{3}