The coefficient of x^n in the expansion of e^ 7 x +e^x e^ 3 x is

Given, $\frac{e^{7 x}+e^x}{e^{3 x}} \Rightarrow e^{4 x}+e^{-2 x}$ Series of $e^a=1+\frac{a}{1!}+\frac{a^2}{2!}+\frac{a^3}{3!} \ldots$$\begin{aligned} \Rightarrow e^{4 x}+ & e^{-2 x}=\left(1+\frac{4 x}{1!}+\frac{(4 x)^2}{2!}+\frac{(4 x)^3}{3!}+\ldots\right) \\ & +\left(1+\frac{(-2 x)}{1!}+\frac{(-2 x)^2}{2!}+\ldots \ldots\right) \end{aligned}$$$Here, coefficient of$$\begin{aligned} & x^2 \equiv \frac{4^2}{2!}+\frac{(-2)^2}{2!} \\ & x^3 \equiv \frac{4^3}{3!}+\frac{(-2)^3}{3!} \\ & \vdots \\ & x^n=\frac{4^n}{n!}+\frac{(-2)^n}{n!} \end{aligned}$$