$\newcommand{\+}{^{\dagger}}% \newcommand{\angles}[1]{\left\langle #1 \right\rangle}% \newcommand{\braces}[1]{\left\lbrace #1 \right\rbrace}% \newcommand{\bracks}[1]{\left\lbrack #1 \right\rbrack}% \newcommand{\ceil}[1]{\,\left\lceil #1 \right\rceil\,}% \newcommand{\dd}{{\rm d}}% \newcommand{\ds}[1]{\displaystyle{#1}}% \newcommand{\equalby}[1]{{#1 \atop {= \atop \vphantom{\huge A}}}}% \newcommand{\expo}[1]{\,{\rm e}^{#1}\,}% \newcommand{\fermi}{\,{\rm f}}% \newcommand{\floor}[1]{\,\left\lfloor #1 \right\rfloor\,}% \newcommand{\half}{{1 \over 2}}% \newcommand{\ic}{{\rm i}}% \newcommand{\iff}{\Longleftrightarrow} \newcommand{\imp}{\Longrightarrow}% \newcommand{\isdiv}{\,\left.\right\vert\,}% \newcommand{\ket}[1]{\left\vert #1\right\rangle}% \newcommand{\ol}[1]{\overline{#1}}% \newcommand{\pars}[1]{\left( #1 \right)}% \newcommand{\partiald}[3][]{\frac{\partial^{#1} #2}{\partial #3^{#1}}} \newcommand{\pp}{{\cal P}}% \newcommand{\root}[2][]{\,\sqrt[#1]{\,#2\,}\,}% \newcommand{\sech}{\,{\rm sech}}% \newcommand{\sgn}{\,{\rm sgn}}% \newcommand{\totald}[3][]{\frac{{\rm d}^{#1} #2}{{\rm d} #3^{#1}}} \newcommand{\ul}[1]{\underline{#1}}% \newcommand{\verts}[1]{\left\vert\, #1 \,\right\vert}$ \begin{align} {\rm E}\pars{x^{n}} &=\int_{-\infty}^{\infty}{1 \over 2\sigma}\, \exp\pars{-\,{\verts{x - \mu} \over \sigma}}x^{n}\,\dd x \\[3mm]&= {1 \over 2\sigma}\bracks{% \int_{-\infty}^{\mu}\exp\pars{x - \mu \over \sigma}x^{n}\,\dd x + \int_{\mu}^{\infty}\exp\pars{\mu - x\over \sigma}x^{n}\,\dd x} \\[3mm]&= {1 \over 2\sigma}\bracks{% \expo{-\mu/\sigma}\sigma^{n + 1} \int_{-\infty}^{\mu/\sigma}\expo{x}x^{n}\,\dd x + \expo{\mu/\sigma}\sigma^{n + 1} \int_{\mu/\sigma}^{\infty}\expo{-x}x^{n}\,\dd x} \\[3mm]&= \half\,\sigma^{n}\bracks{% \expo{-\mu/\sigma}\pars{-1}^{n + 1} \int_{\infty}^{-\mu/\sigma}\expo{-x}x^{n}\,\dd x + \expo{\mu/\sigma} \int_{\mu/\sigma}^{\infty}\expo{-x}x^{n}\,\dd x} \\[3mm]&= \half\,\sigma^{n} \expo{-\mu/\sigma}\pars{-1}^{n + 1} \bracks{-\Gamma\pars{n + 1} + \gamma\pars{n + 1,-\,{\mu \over \sigma}}} \\[3mm]&\phantom{=}+ \\[3mm]&\phantom{=} \half\,\sigma^{n}\expo{\mu/\sigma} \bracks{-\gamma\pars{n + 1,{\mu \over \sigma}} + \Gamma\pars{n + 1}} \\[3mm]&= \half\sigma^{n}\bracks{\pars{-1}^{n}\expo{-\mu/\sigma} + \expo{\mu/\sigma}} \Gamma\pars{n + 1} \\[3mm]&\phantom{=}+ \\[3mm]&\phantom{=} \half\sigma^{n}\bracks{% \expo{-\mu/\sigma}\pars{-1}^{n + 1}\gamma\pars{n + 1,-\,{\mu \over \sigma}} - \expo{\mu/\sigma}\gamma\pars{n + 1,{\mu \over \sigma}}} \end{align} where $\Gamma\pars{z}$ is the Gamma function and $\gamma\pars{\alpha,z}$ is an incomplete gamma function.
$\Gamma\pars{2009 + 1} = 2009!$. The $\gamma$'s are approximated by $ \gamma\pars{\alpha,x} \approx {x^{\alpha} \over \alpha} $ when $\alpha \gg 1$. Then $ \gamma\pars{2009 + 1,\pm\,{\mu \over \sigma}} \approx {\pars{\pm\,\mu/\sigma}^{2010} \over 2010} $