Number of outcomes possible for best-of-nine series

How many different outcomes are there in a best-of-nine series between two teams A and B? Generalize to a best-of-n series where n is odd.

xxxxA xxxxxA xxxxxxA xxxxxxxA xxxxxxxxA

$\displaystyle \left({4\atop 4}\right)+\left({5\atop 4}\right)+\left({6\atop 4}\right)+\left({7\atop 4}\right)+\left({8\atop 4}\right)= $the number of outcomes where A wins the series. Multiply this by two to get number of outcomes where A or B wins the series. For best-of-n where n is odd

$\displaystyle

2*\sum_{k=\frac{n-1}{2}}^{n-1}\left({k\atop \frac{n-1}{2}}\right)

$

Does this look correct?