Limit with Factorials

1. Apr 8, 2010

pseudogenius

Anyone know of any method to evaluate this limit,

$$\lim_{n \to \infty} \frac{n!}{\left(\frac{n+p}{2}\right)!\left(\frac{n-p}{2}\right)!}2^{-n}$$

it seems to go to zero, but I have no way to be sure.

2. Apr 8, 2010

Hurkyl

Staff Emeritus
What did you get from Stirling's approximation?