User blog comment:MilkyWay90/Finishing my very first notation - The Generalized Factorial/@comment-35470197-20190710234255/@comment-35470197-20190713232510

Again \(@\)'s should be \(@_n\)'s. Moreover, the last rule includes an actual loop because \(F_!(@,!,@,!,@)\) appears in the expansion of \(F_!(@,!,@,!,@)\).