f(2x) - f(x) - 1 = a(x - 1)(x - 2)(x - 4)(x - 8)(x - 16)(x - 32)(x - 64)
x = 0 代入可求出 a
所求即其一次項係數

f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0
f(2x) - f(x) - 1 的一次項係數 = 2a_1 - a_1 = a_1 = f(x) 的一次項係數

f(2x) - f(x) - 1 = a(x - 1)(x - 2)(x - 4)(x - 8)(x - 16)(x - 32)(x - 64)
x = 0 代入可得
-1 = a(-1)(-2)(-4)(-8)(-16)(-32)(-64)
a = 1/(1 * 2 * 4 * 8 * 16 * 32 * 64)

f(2x) - f(x) - 1 = (x - 1)(x - 2)(x - 4)(x - 8)(x - 16)(x - 32)(x - 64)/(1 * 2 * 4 * 8 * 16 * 32 * 64)
f(2x) - f(x) - 1 的一次項係數 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 = 127/64