Show that the solution to $T(n) = 2T(\lfloor n/2 \rfloor + 17) +n$ is $O(n \lg n)$.

The trick is to subtract the constant from assumption that has been added in the recursion to reduce it down to a more familiar form.

Let us assume $T(n) \le c (n - 17) \lg (n - 17)$ for all $n \ge n_0$, where $c$ and $n_0$ are positive constants.

The last step holds as long as $c \ge 1$.