The sequence A000975 in the Encyclopedia of Integer Sequences can be defined by A₁ = 1, A_n+1 = 2A_n if n is odd, and A_n+1 = 2A_n+1 if n is even. This sequence satisfies other recurrence relations, admits some closed formulas, and is known to enumerate several interesting families of objects. We provide a new interpretation of this sequence using a binary operation defined by a ⊖ b := -a - b. We show that the number of distinct results obtained by inserting parentheses in the expression x₀ ⊖ x₁ ⊖ · · · ⊖ x_n equals A_n, by investigating the leaf depth in binary trees. Our result can be viewed as a quantitative measurement for the nonassociativity of the binary operation .