[math-fun] Parenthesizing

Apropos of parenthesizing exponential towers, here's an easier question (probably not new): Look at all the (Catalan-many) ways to parenthesize a_1 - a_2 - ... - a_n. Not all are distinct as linear functions of a_1, a_2, ..., a_n; e.g., (a - (b - c)) - d = a - (b - (c - d)). How many different functions can be obtained? I don't know the answer. Is it 2^(n-2)? Jim Propp