Your Gamma function is inaccurate. 2.5! is 3.323350970. Try it

$$\small{\text{$ 2.5! = \Gamma{(2.5+1)} $ }}$$

$$\small{ \text{ Formula } \boxed{ \begin{array}{lcl} \Gamma{(x+1)} = x\cdot\Gamma{(x)} \\ \Gamma{(\frac12)} = \sqrt{\pi} \end{array} } }$$

$$\small{ \begin{array}{lcl} 2.5!&=& \Gamma{(2.5+1)}\\ &=& 2.5\cdot\Gamma{(2.5)}\\ &=& 2.5\cdot \Gamma{(1.5+1)}\\ &=& 2.5\cdot 1.5\cdot \Gamma{(1.5)}\\ &=& 2.5\cdot 1.5\cdot \Gamma{(\frac12+1)}\\\\ &=& 2.5\cdot 1.5\cdot \frac12 \cdot \Gamma{(\frac12)}\\\\ &=& 2.5\cdot 1.5\cdot \frac12 \cdot \sqrt{\pi}\\\\ &=& 1.875 \cdot \sqrt{\pi} \\ &\approx& 1.875 \cdot 1.77245385091 \\ \mathbf{2.5!} &\mathbf{\approx}& \mathbf{3.32335097045} \end{array} }$$

Thanks for letting us know,

Yes Wolfram|Alpha agrees with your figure of 3.32335...  (maybe that is where you got?)

http://www.wolframalpha.com/input/?i=2.5%21

web2.0 calc

$${\mathtt{2.5}}{!} = {\mathtt{3.320\: \!382\: \!507\: \!505\: \!424}}$$

I don't know where else to look it up.

It is most likely a rounding error.

I will leave a note for admin.    

Thanks Heureka :)

 It's usually calculated using an Integral of (x^(n-1).e^-x) for all x from 0 to infinity. 1/2 is a special case. The Integral works for any number, i.e. 2.5, 3.123, 11.534....etc.