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Sequence factorial of g-gonal numbers

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.