Three types of functions in one!

We know that $\displaystyle {e}^{x} = \sum_{n=0}^{\infty}{\frac{{x}^{n}}{n!}}$

Differentiating w.rt. $x$ and then multiplying by $x$ ,

$\displaystyle x{e}^{x} = \sum_{n=0}^{\infty}{\frac{n{x}^{n}}{n!}}$

Again differentiating w.r.t $x$ and multiplying by $x$ ,

$\displaystyle x(x{e}^{x} + {e}^{x}) = \sum_{n=0}^{\infty}{\frac{{n}^{2}{x}^{n}}{n!}}$

Substituting $x=2$ ,

$\displaystyle \sum_{n=0}^{\infty}{\frac{{n}^{2}{2}^{n}}{n!}} = 6{e}^{2}$

Floor (44.3343365935839) = 44