How to find the coefficient of $x^{203}$ in the expansion of $(x-1)(x^2 - 2)(x^3-3)\dots(x^{20} - 20)$? 
How to find the coefficient of $x^{203}$ in the expansion of $(x-1)(x^2 - 2)(x^3-3)\dots(x^{20} - 20)$?

I took $x$ as common from each bracket making $x^{190}$ but I don't understand what to do next. Please help.

The ways of writing $7$ as a sum of distinct positive integers are $7,1+6,2+5,3+4,1+2+4$, so the coefficient of $x^{203}$ will be $-7+1\cdot 6 + 2\cdot 5 + 3 \cdot 4 - 1\cdot 2 \cdot 4 = 13$.
