Double Factorial (n!!) Calculator

Enter an integer n to compute the double factorial n!! (n·(n-2)·(n-4)…) exactly. See the parity, the relation to the ordinary factorial n!, the digit count, and scientific notation at a glance.

Input

Enter an integer n to compute the double factorial n!!. For even n it multiplies n·(n-2)…2, for odd n it multiplies n·(n-2)…1. Here 0!!=1 and (-1)!!=1.

Integer n

Enter an integer of -1 or greater (both -1 and 0 give the value 1).

Result

Value of 9!!

945

Parity

Odd

Number of digits

Scientific notation

9.450000e+2

Relation to the ordinary factorial

Ordinary factorial 9!	362,880
Partner double factorial (9-1)!!	384
Identity that holds	9! = 9!! × (9-1)!!

Growth in digit count (log10 scale)

How it works

The double factorial n!! multiplies only the positive integers with the same parity as n, stepping by two. For even n it equals n·(n-2)·(n-4)…4·2, and for odd n it equals n·(n-2)·(n-4)…3·1.
By convention 0!!=1 and (-1)!!=1. These base cases keep the usual recurrences and identities consistent.
The double factorial relates to the ordinary factorial through n! = n!! · (n-1)!! for n at least 1. This tool also reports the partner value (n-1)!!.
Products are accumulated with big integers, so the exact value is returned even for many digits. When the number is very large it is shown in scientific notation for readability.
Odd double factorials of the form (2k-1)!! appear often and can be written as (2k)!/(2^k·k!). They show up frequently in probability, combinatorics, and special-function formulas.

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