0 is correct pragmatacally, and makes the puzzle harder for those not wise that 0!=1 by the definition of factorial. (as opposed to proof.... factorial being a shorthand for math and ths being convenient. if there were a proof it would be a theorem, which its not.)
i knew factorial but i had to read up on 0!, news to me too.
on another note, without context, we could say there is an infinite set of functions that satisfy any such question.
"what could come next and why" or something.
edit: 1 is indeed correct for the sequence, ignore that part... my bad.