Related Function:

The FACTDOUBLE function returns the double factorial of a number.

Syntax

=FACTDOUBLE(number)

Arguments

Argument Description
number The value for which to return the double factorial

  If number is not an integer, it is truncated

Examples

  A B C
1 Formula Result Notes
2 =FACTDOUBLE(5) 15 Double factorial of 6. For 6, an even number, the double factorial is equivalent to 5*3*1
3 =FACTDOUBLE(6) 48 Double factorial of 6. For 6, an even number, the double factorial is equivalent to 6*4*2; using the equation: n!! = n*(n-2)*(n-4)…(4)(2)
4 =FACTDOUBLE(7) 105 Double factorial of 7. For 7, an odd number, the double factorial is equivalent to 7*5*3*1; using the equation: n!! = n*(n-2)*(n-4)…(3)(1)
5 =FACTDOUBLE(8) 384 Double factorial of 8. For 8, an even number, the double factorial is equivalent to 8*6*4*2

Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if the supplied number argument is not recognized as a numeric value
#NUM! Occurs if the supplied number argument is < 0

The double factorial of a number, n!!, is the product of all the integers from 1 up to some non-negative integer n that have the same parity as n. That is,     

    \[   n!! = \prod_{k=0}^m (n-2k) = n(n-2)(n-4) \cdots    \]

where m = \lceil n/2 \rceil - 1

For example:

  • 5!! = 1 x 3 x 5 = 15
  • 6!! = 2 x 4 x 6 = 48

The double factorial of a number is calculated as follows:

For even n, the double factorial is

    \[   n!! = \prod_{k=1}^{n/2}(2k) = n(n-2) \cdots 2    \]

For odd n, the double factorial is

    \[    n!! = \prod_{k=1}^{(n+1)/2} (2k - 1) = n(n-2) \cdots 1    \]

See Wikipedia for more information on Factorial.