A few things that make the number way larger than you might think at first:
- If the game has Ruins, then you have a different setup depending on which Ruins are in the Ruins pile. This would also depend on the number of players, so you would have to decide if you consider a setup for a 2 player game to be a different setup than a 4 player game. Not only is it which Ruins are chosen, but the order that the Ruins are in is a different game.
- The order that the Knights are in make for a different game, so games with Knights have 10! possible ways of having those Knights.
- The order of the Black Market deck makes for a different game. Since you can fill the Black Market deck however you want, not only do you need 2^(every card not in the Kingdom) ways to fill the Black Market deck, but then you have to multiply each of those possibilities by the number of cards in the deck factorial.
- If you do include Adventures, then remember that the limit of 2 events is only a suggestion, you can play with 2^20 possible combinations of events (including the no events option).
- Something that would actually lower the number of setups: by the official rules, you can't have Platinum/Colonies unless you have at least 1 Prosperity card. Similar for Shelters and Dark Ages.