It is required to obtain the $E[(X+1)!]$ where $X$ follows the Poisson distribution with the parameter $\lambda$.
My approach
The given Expectation can be written in the following form:
$E[(X+1)!]=E[(X+1)X]=E(X^2+X)=E(X^2)+E(X)$
Is my approach correct? I am not sure. I have done this as $x$ can take only non negative Values.