Write an equation for the sequence: 2, 24, 720, 40320, 3628800

The sequence forms a group of factorials.

Notice that

2! = 2

4! = 24

6! = 720

8! = 40320

10! = 3628800

Each number beside a factorial is an even number. The equation for even number is 2x. Therefore, the final equation is

f (x) = 2x!

Verify

x = 1, f (1) = 2 (1) ! = 2!

x = 2, f (2) = 2 (2) ! = 4!

x = 3, f (3) = 2 (3) ! = 6!

and so on.