Python, 4343 38
import math
deff=lambda f(n):return math.gamma(n+1)
Explanation: The gamma function is a very quickly-growing complex function which, at integer values, is equal to the factorial of one less than the number. So we add one to n and take the gamma function of it.
I hope this isn't considered cheating, since the gamma function is not technically able to directly calculate the factorial.