The coefficient of $x^n$ in $\large\frac{1-2x}{e^x}$ is :

Question

\[\begin {array} {1 1} (a)\;\frac{(1+2n)}{n !} & \quad (b)\;(-1)^n. \frac{1+2n}{n!} \\ (c)\;(-1)^n.\frac{(1-2n)}{n!} & \quad (d)\;(-1)^n.\frac{(1+4n)}{n!} \end {array}\]