1. Let $n(n>2), Y_{n}=\{2,3, \cdots, n\}$. For each non-empty subset $A$ of $Y_{n}$, let $T(A)$ be the product of all elements in $A$. Find $\sum_{A \subseteq Y_{n}} T(A)$.
(提示: Construct the function $f(x)=\sum_{1 \leq Y_{n}} T(A) x^{n-|A|-1}$. Then $\left.\sum_{A \leq Y_{n}} T(A)=f(1)=\frac{1}{2}(n+1)!-1.\right)$