Time complexity of combinations of n pairs of parentheses
Actually, for every combination of parenthesis, your algorithm performs $\Theta(n)$ amount of work (to build the string and append it to your list of combinations).

The number of valid combinations of $n$ pairs of parenthesis is the $n$'th Catalan Number $C_n = \frac{1}{n+1}\binom{2n}{n}$.

Thus, your algorithm runs in $\Theta(nC_n)$ which is also equal to $\Theta(\frac{4^n}{\sqrt{n}})$, because $C_n$ grows as $\Theta(\frac{4^n}{n^{3/2}})$ (see the linked Wikipedia article).