Can't Install App on Ipod Touch?

[cullenand]

I bought an app from the app store on my ipod touch and once it finished installing, it said that my ipod didnt have enough memory left. I deleted some of my videos and then went to the app store to try and download it again but it said that it was already installed. When it said that i didnt have enough memory it deleted the app from my ipod. Can somebody tell me how to install this app?

 

[Sureboss]

When you deleted stuff from your iPod did you re-sync it?