\displaystyle {\frac {291}{400}}+{\frac {9}{200}}\,{n}^{2}+{\frac {421}{1200}}\,n+{ \frac {1}{600}}\,{n}^{3}+\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 }^{-n-1}+\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}+17\,{\alpha}^{4}+9 \,{\alpha}^{3} \right) {\alpha}^{-n-2} \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}+{\alpha}^{4}-27\,{\alpha}^{3} \right) {\alpha}^{-n-1}