We know that partial summation states that given two sequences $(\alpha_n), (\beta_n)$, we can write
$$\sum_{n=1}^p\alpha_n\beta_n=\beta_nA_p+\sum_{n=1}^{p-1}(\beta_n-\beta_{n+1})A_n$$
where $A_p=\sum_{n=1}^{p}\alpha_n$.
Is there a version of this formula for sequences $(\alpha_n^m)$ with two indexes?