User blog comment:Alejandro Magno/A Little Factorial Extension/@comment-5029411-20141001004726

n!!! = n!(((...((!)!)!...)!)!)! with n !'s

n!!!! = n!(((...((!!)!!)!!...)!!)!!)!! with n !!'s

n!! 2 = n!!!!...!!! with n !'s

n!! ! = n!! n with n !'s