Memoized version:

  class Factorial(object):
    def __init__(self):
        self.n = 0
        self.fact_n = 1

    def next_fact(self):
        self.fact_n *= (self.n + 1)
        self.n += 1

    def prev_fact(self):
        self.fact_n /= self.n
        self.n -= 1

    def fact(self, n):
        if n == self.n:
            return self.fact_n
        elif n > self.n:
            # start from self.n working forward
            self.next_fact()
            return self.fact(n)
        else:
            # start from fact_n working backwards
            self.prev_fact()
            return self.fact(n)


  fobj = Factorial()
  print fobj.fact(6)
  print fobj.fact(8)
  print fobj.fact(3)