记:
\[na_1+(n-1)a_{2}+(n-3)a_3+...+2a_{n-1}+a_{n}=T_{n}\]
\[n^2a_1+(n-1)^2a_2+(n-3)^2a_3+...4a_{n-1}+a_{n}=Q_{n}\]
\[n^3a_1+(n-1)^3a_2+(n-3)^3a_3+...8a_{n-1}+a_{n}=R_{n}\]
\[S_{n}=\sum a_{n}\]
则有:
\[T_{n}+S_{n}+a_{n+1}=T_{n+1}\]
\[Q_{n}+2T_{n}+S_{n}+a_{n+1}=Q_{n+1}\]
\[R_{n}+3Q_{n}+3T_{n}+S_{n}+a_{n+1}=R_{n+1}\]
\[na_1+(n-1)a_{2}+(n-3)a_3+...+2a_{n-1}+a_{n}=T_{n}\]
\[n^2a_1+(n-1)^2a_2+(n-3)^2a_3+...4a_{n-1}+a_{n}=Q_{n}\]
\[n^3a_1+(n-1)^3a_2+(n-3)^3a_3+...8a_{n-1}+a_{n}=R_{n}\]
\[S_{n}=\sum a_{n}\]
则有:
\[T_{n}+S_{n}+a_{n+1}=T_{n+1}\]
\[Q_{n}+2T_{n}+S_{n}+a_{n+1}=Q_{n+1}\]
\[R_{n}+3Q_{n}+3T_{n}+S_{n}+a_{n+1}=R_{n+1}\]
