Find the co-efficient of $x^{18}$ in the expansion of $(x+1)(x+2)...(x+10)(2x+1)(2x+3)...(2x+19)$. 
Find the co-efficient of $x^{18}$ in the expansion of
  $$(x+1)(x+2)...(x+10)(2x+1)(2x+3)...(2x+19)$$

What I've done :
$$
(x+1)(x+2)...(x+10)(2x+1)(2x+3)...(2x+19)
\\
=\frac{(2x+1)(2x+2)(2x+3)...(2x+20)}{2^{10}}
$$
I can't think of any way to find the coefficient of $x^{18}$ in this expansion. What am I doing wrong ?

Now to get a term with $x^{18}$ you have to choose $18$ of the $2x$ terms and two of the constant terms, so your term in the numerator is $$(2x)^{18}\sum_{i=1}^{19}\sum_{j=i+1}^{20} ij$$
