The gamma function, which has the property to interpolate the factorial whenever the argument is an integer, is a special case (the case "g"?=?2) of the general term of the sequence factorial of "g"-gonal numbers. In relation to this special case, a formula for calculating the general term of the sequence factorial of any "g"-gonal number was obtained after considering some specific cases. Important properties on functional equations of "g"-gonal sequence factorials are derived. (Contains 1 table.)