That's kind of your unfortunate moment there, as if there are no backups there is nothing linode is going to be able to do for you (especially if you aren't on a managed plan).

Good chance you're kinda screwed, very very rare chance you might be able to recover it roughly using something like extundelete, but what exactly it can recover will quite largely depend on how long it's been since the DB was physically deleted and even if it was only deleted moments ago you still may end up with missing bits.

Out of sheer chance, are you sure it was deleted? And that the database schema/tables didn't simply get corrupted some how? Or maybe the user account?