gamma function algebra...

Wasn't sure which forum to put this in, I've done the probability part - it's just that my answer is a few lines away from the sample solution I've been given, and I don't understand what they've done.

My answer is

$\displaystyle (2^k/sqrt(pi))(k - 1/2)(k - 3/2) ... ... (3/2)(1/2)Gamma(1/2)$

The next line of working for the sample solution is

$\displaystyle (2k - 1)(2k - 3) ... ... (3)$

I see that the sqrt(pi) and the gamma(1/2) cancel, other than that I'm stuck! :(

Any help would be much appreciated. not sure if it's needed or not, but k = n/2 where n is an positive even integer