Solve summation of $\sum_{j=0}^{n-2}2^j (n-j)$ Question
While Solving a recursive equation , i am stuck at this summation and unable to move forward.Summation is 

$$\sum_{j=0}^{n-2}2^j (n-j)$$

My Approach

$$\sum_{j=0}^{n-2}2^j (n-j) = \sum_{j=0}^{n-2}2^j \times n-\sum_{j=0}^{n-2} 
2^{j} \times j$$

$$=n \times (2^{n-1}-1)-\sum_{j=0}^{n-2} 
2^{j} \times j$$
I am unable to move forward , please help me out!

Hint
Consider $$\sum_{i=0}^p i x^i=x\sum_{i=0}^p i x^{i-1}=x\left(\sum_{i=0}^p  x^i \right)'$$
