$\sum \limits _{n=1}^{\infty} \large\frac{2n^2+n+1}{n !}$ is equal to :

Question

$$\begin {array} {1 1} (a)\;2e-1 & \quad (b)\;2e+1 \\ (c)\;6e-1 & \quad (d)\;6e+1 \end {array}$$