User blog comment:GamesFan2000/Extended Factorial Notation/@comment-31966679-20181111194101

In order to keep the properties of the factorial still in the extended factorial, you can define n!a = n! * n-1! * n-2 ... n-a!

Or, to keep this easier to evaluate in the FGH, you could do n!a = n!!!!...!!!! with a factorials