If you purchased Yummy FTP directly in the application itself (ie you didn't purchase from our website) then Yummy FTP automatically entered your registration details for you after the purchase was completed. When registered, the 'Enter Serial Number' option is removed, which is probably why you can't find it

So, it sounds like you're already registered. You can check by looking at the About window - select 'About Yummy FTP' from the Yummy FTP menu and you'll see (Registered) if you are.