Input / Output pattern help please?

Question

I'm doing a math paper which requires me to find the pattern and formula for the following input/output function. Any help would be greatly appreciated.
input 2 output 1
input 3 output 2
input 4 output 4
input 5 output 8
input 6 output 16
input 7 output 48
input 8 output 80

(yes, I know the first few double, but that isn't consistent with the rest)

Answer 1

The closest I could find is at the reference below; however, it's pretty esoteric and surely NOT what your teacher is looking for.