The double factorial function

To calculate $n!!$ for odd $n$ , simply loop over the odd integers up to and including $n$ , multiplying them together:

# Calcualate n!! = 1.3.5.7...(n-2)n for odd n
n = 11
dfactorial = 1
for i in range(3, n+1, 2):
    dfactorial *= i
print('{:d}!! = {:d}'.format(n, dfactorial))

For even $n$ , note that $n!! = \prod_{i=1}^{n/2} (2i) = 2^{n/2} (n/2)!,$ so:

# Calcualate n!! = 2.4.6.8...(n-2)n for even n
import math
n = 10
dfactorial = 2**(n // 2) * math.factorial(n // 2)
print('{:d}!! = {:d}'.format(n, dfactorial))

The double factorial function

Solution P2.4.6