7. Let $A$ denote the set of all non-empty subsets of the set $\{1,2, \cdots, n\}$. For $a \in A$, let $\delta(a)$ denote the sum of the elements in $a$. Find $\sum_{a \in A} \delta(a)$.
7. $2^{n-2} n(n+1)$.

The above text has been translated into English, retaining the original text's line breaks and format.