Problem : 

The coefficient of $x^{15}$ in the product $(1-x)(1-2x)(1-2^2x)(1-2^3x)\cdots (1-2^{15}x)$ is 

(a) $2^{105}-2^{121}$ 

(b) $2^{121}-2^{105}$ 

(c) $2^{120}-2^{104}$ 

(d) $2^{110}-2^{108}$

My approach : 

Tried to find pattern if any in the given expansion, so expanded first three terms : 

$(1-x)(1-2x)(1-2^2x) = (1-3x+2x^2)(1-4x) = (1-3x+2x^2 -4x+12x^2 -8x^3)$

$= (1-7x+14x^2 -8x^3)$

But didn't find any pattern of this series please suggest how to proceed will be of great help thanks.