What is the sum of the following sequence
$\begin{align*} (2^1 - 1) &+ \Big((2^1 - 1) + (2^2 - 1)\Big)\\ &+ \Big((2^1 - 1) + (2^2 - 1) + (2^3 - 1) \Big)+\ldots\\ &+\Big( (2^1 - 1)+(2^2 - 1)+(2^3 - 1)+\ldots+(2^n - 1)\Big) \end{align*}$
I tried to solve this. I reduced the equation into the following equation
$n(2^1) + (n-1)\cdot2^2 + (n-2)\cdot2^3 +\ldots$
but im not able to solve it further. Can any one help me solve this equation out. and btw its not a Home work problem. This equation is derived from some puzzle.
Thanks in advance