Fast Modular Factorial?

A small question about large integer math... We are all familar with the fact that x^(2^n) mod p may be evaluated with only n modmults which accumulate geometrically increasing powers of x. Does a similar fast algorithm exist for computing (2^n)! mod p? The only difference here is that one is accumulating a huge product of consecutive integers instead of the same integer multiplied many times. I am interested in values of n around several hundred. I have played with this quite a bit and am unable to see any easy exploitable symmetry which would lead to an efficient algorithm. Any ideas? -- Mike Duvos $ PGP 2.6 Public Key available $ mpd@netcom.com $ via Finger. $