Find coefficients of $x^{2012}$ in $(x+1)(x^2+2)(x^4+4)\cdots (x^{1024}+1024)$ Find coefficients of $x^{2012}$ in $(x+1)(x^2+2)(x^4+4)\cdots (x^{1024}+1024)$
Attempt:  i have break $2012$ in to sum of power of $2$
as $2012 = 2^{10}+2^{9}+2^{8}+2^7+2^6+2^4+2^3+2^2$
but wan,t be able to go further, could some help me , thanks

$2012 = 2047 - 35 = (\sum_{k=0}^{10}{2^k}) - 35$
$35 = 2^5+2^1+2^0 => 2012 = 2^{10}+2^9+2^8+2^7+2^6+2^4+2^3+2^2$
So this means that the for the parenthesis with the power of $x$ in this set: ${10, 9, 8, 7, 6, 4, 3, 2}$, the part with $x$ is multiplied. So for the rest of the parenthesis, the number is chosen. So the coefficient of $x^{2012}$ is:
$2^5*2^1*2^0 = 2^6 = 64$
