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.
