This loop is fueled by Ashnod's Altar, which provides the initial sacrifice outlet to send Prosperous Innkeeper to the graveyard and generate the raw mana we need. That death triggers Nim Deathmantle, letting us pay four mana to pull Prosperous Innkeeper right back to the battlefield while reattaching the Equipment to it. The magic happens because Doubling Season sees Prosperous Innkeeper re-enter and doubles its token creation, spitting out two Treasure tokens instead of just one. Sacrificing those two Treasures back to Ashnod's Altar conveniently funds the Nim Deathmantle tax, leaving you with an endless cycle of infinite life gain, enter-the-battlefield triggers, and sacrifices.