I'm sure I've seen factorial algorithms in Python,
I just can't recall where at the moment.  Why don't
you try doing a search of past newsgroup archives
and then the web site for "factorial", at
www.python.org?  Are you using Python longs for
the numbers, by the way--if you suffix constants
with a "L", your integers should be able to grow
very large without an overflow.  Here's something
that isn't necessarily optimal or correct, but shows
longs at work:



>>> 5 * 4 * 3 * 2 * 1
120
>>> fact(5)
120L


>>> range(2, 5+1), range(5, 1, -1)
([2, 3, 4, 5], [5, 4, 3, 2])


-----------------

>>> def fact(N):
...     res = 1L
...     for i in range(N, 1, -1):
...         res = res * i
...     return res
...
>>> fact(0)
1L
>>> fact(1)
1L
>>> fact(3)
6L
>>> fact(4)
24L
>>> fact(5)
120L
>>> fact(10)
3628800L
>>> 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2
3628800
>>> fact(20)
2432902008176640000L
>>> fact(40)
815915283247897734345611269596115894272000000000L
>>>



------------------

>>> def fact(N):
...     res = 1L
...     for i in range(2, N+1):
...         res = res * i
...     return res
...
>>> fact(0)
1L
>>> fact(1)
1L
>>> fact(2)
2L
>>> fact(4)
24L
>>> fact(5)
120L
>>> fact(10)
3628800L
>>> fact(20)
2432902008176640000L
>>>



---------------------


>>> def fact(N):
...     if N <= 1:
...         return 1L
...     else:
...         return N * fact(N-1)
...
>>> fact(4)
24L
>>> fact(5)
120L
>>> fact(10)
3628800L
>>> fact(20)
2432902008176640000L 


-----------------------------------------------------


>>> def fact(N):
...     res = 1
...     for i in range(N, 1, -1):
...         res = res * i
...     return res
...
>>> fact(4)
24
>>> fact(5)
120
>>> fact(10)
3628800
>>> fact(20)
Traceback (innermost last):
  File "<stdin>", line 1, in ?
  File "<stdin>", line 4, in fact
OverflowError: integer multiplication



>>> def fact(N):
...     res = 1L
...     for i in range(N, 1, -1):
...         res = res * i
...     return res
...
>>> fact(0)
1L
>>> fact(1)
1L
>>> fact(4)
24L
>>> 4 * 3 * 2
24
>>> fact(5)
120L
>>> fact(10)
3628800L
>>> fact(20)
2432902008176640000L
>>> fact(40)
815915283247897734345611269596115894272000000000L
>>> range(4, 1, -1)
[4, 3, 2]



>>> def fact(N):
...     res = 1.0
...     for i in range(N, 1, -1):
...         res = res * i
...     return res
...
>>> fact(5)
120.0
>>> fact(10)
3628800.0
>>> fact(20)
2.43290200818e+018
>>> fact(40)
8.15915283248e+047
>>> fact(0)
1.0


---------------------------------------------


>>> def fact(N):
...     if N <= 1:
...         return 1
...     else:
...         return N * fact(N-1)
...
>>> fact(4)
24
>>> fact(5)
120
>>> fact(10)
3628800
>>> fact(20)
Traceback (innermost last):
  File "<stdin>", line 1, in ?
  File "<stdin>", line 5, in fact
  File "<stdin>", line 5, in fact
  File "<stdin>", line 5, in fact
  File "<stdin>", line 5, in fact
  File "<stdin>", line 5, in fact
  File "<stdin>", line 5, in fact
  File "<stdin>", line 5, in fact
  File "<stdin>", line 5, in fact
OverflowError: integer multiplication



>>> def fact(N):
...     if N <= 1:
...         return 1L
...     else:
...         return N * fact(N-1)
...
>>> fact(0)
1L
>>> fact(1)
1L
>>> fact(4)
24L
>>> fact(5)
120L
>>> fact(10)
3628800L
>>> fact(20)
2432902008176640000L
>>> fact(40)
815915283247897734345611269596115894272000000000L