I think It should be
$\binom{n}{1}$ + $\binom{n}{2}$ + $\binom{n}{3}$ + ...............+ $\binom{n}{n-1}$
= 2n - $\binom{n}{0}$ - $\binom{n}{n}$
= 2n - 2
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Otherwise you can also think of it like this: Distributing 'n' different balls into 2 distringuishable boxes
Thus, answer = S(n, 2) * 2!
Just try n=3. The answer matches with above solution.
