Expected Weight

Given a sequence $A$ of length $N$, the weight of this sequence is defined as $$\text{weight}(A) = \sum_{i = 1}^{N} i\cdot A_i$$ Given an integer $N$, we pick a permutation $A$ of $[1, 2 \dots N]$ uniformly at random. What is the expected weight of this permutation? It can be shown that the answer can be represented as $\displaystyle \frac{P}{Q}$ where $P$ and $Q$ are coprime integers and $Q \n