Double Factorial Calculator n!!

What is Double Factorial?

The double factorial, denoted as n!!, is a specialized mathematical operation that extends the concept of the standard factorial. It is defined as the product of all integers from 1 up to n that have the same parity (odd or even) as n.

How to Calculate Double Factorial

To calculate the double factorial:

• For even n: multiply all even numbers from 2 to n
• For odd n: multiply all odd numbers from 1 to n

Formula

The formula for double factorial is:

\[ n!! = \begin{cases} n \times (n-2) \times (n-4) \times ... \times 4 \times 2, & \text{if n is even} \\ n \times (n-2) \times (n-4) \times ... \times 3 \times 1, & \text{if n is odd} \end{cases} \]

Calculation Steps

1. Determine if n is odd or even
2. Start with n
3. Multiply by (n-2)
4. Continue multiplying by numbers decreasing by 2 each time
5. Stop when you reach 2 (for even n) or 1 (for odd n)

Examples

Let's calculate some double factorials:

• 5!! = 5 × 3 × 1 = 15
• 6!! = 6 × 4 × 2 = 48
• 7!! = 7 × 5 × 3 × 1 = 105
• 8!! = 8 × 6 × 4 × 2 = 384

These examples demonstrate how the calculation differs for odd and even numbers in double factorials.