Im stuck at here
$\begin{align*} T(n)&= 2^n T(n-1)+c \\ T(n-1)&= 2^{n-1} T(n-2)+c \\ T(n-2)&= 2^{n-2} T(n-3)+c \\ ..\\ ..\\ T(n)&= 2^{n} T(n-1)+c \\ &= 2^{n} [2^{n-1} T(n-2)+c]+c\\ &= 2^{n} 2^{n-1} T(n-2)+2^{n}c+c \\ &= 2^{n} 2^{n-1} [2^{n-2} T(n-3)+c]+2^{n}c+c\\ &= 2^{n} 2^{n-1} 2^{n-2} T(n-3)+ 2^{n} 2^{n-1}c+2^{n}c+c \\ &= 2^{n+(n-1)+(n-2)+..+1} T(n-k) +[ 2^{n+(n-1)+(n-2)+..+1}+2^{n+(n-1)+(n-2)+..+2}+...+2^{n}]c\\ &=2^{\frac{n(n+1)}{2}} ?? \end{align*}$
Now, multiplying and diving to take out common term
$\begin{align*} [ 2^{n+(n-1)+(n-2)+..+1}+2^{n+(n-1)+(n-2)+..+2}+...+2^{n}] \\ =& 2^{n+(n-1)+(n-2)+..+1}[\frac{1}{1}+\frac{1}{1.2}+\frac{1}{3!}...+\frac{1}{(2^{n})!}]\\ =&2^{\frac{n(n+1)}{2}}[\sum_{i=1}^{2^n}\frac{1}{i !}] \end{align*}$
How to proceed further
