If $a_k$ is the coefficient of $x^k$ in the expansion of $(1+x+x^2)^n$ for $k=0,1,2.......,2n$ then $a_1+2a_2+3a_3+.....+2na_{2n}$ is equal to

Question

$$\begin {array} {1 1} (a)\;-a_0 & \quad (b)\;3^n \\ (c)\;n.3^{n+1} & \quad (d)\;n.3^n \end {array}$$