n! is the product of all integers from 1 through n. For example, 2!=1*2, 3!=1*2*3, 4!=1*2*3*4, and
so on. The double factorial n!! is not the same as the repeat factorial, say, (3!)!=6!=1*2*3*4*5*6.
n!! is best computed backwards. It's the product of all positive integers starting with n and picking up
only every other integer. For example, 6!!=6*4*2=48. 5!!=5*3*1. Therefore, I correctly claim that
31=4!!*4-4/4 since 4!!=4*2=8.
Hope this helps.