I don't understand how to deal with sequences like following:

$\displaystyle a_n=\frac{1\cdot 3\cdot 5\cdot...\cdot (2n-1)}{(2n)^n}$

It's not clear what the first term would be, or whether it converges. I want to list terms to see what is happening. If I write $\displaystyle a_k=\frac{(2k-1)^k}{(2k)^k}$ it is clear that the denominator increases at a faster rate as $\displaystyle k->\infty$, but I still can't tell what the entire sequence is going to do.