Rewriting $n(2^{2^{n-1}}-1)-2^{2^n}+2^{2^{n-1}+1}$

Question

Could you help me to write in a better way the following expression? (by better I mean for example simplifying if I can) $$ n(2^{2^{n-1}}-2)-2^{2^n}+2^{2^{n-1}+1} $$

Answer 1

$$n(2^{2^{n-1}}-2)-2^{2^n}+2^{2^{n-1}+1} = 2^{2^{n-1}}(n+2-2^{2^{n-1}})-2n$$