The Seven Doubles, how does one permute them? Two stones build two houses,
three build six houses, four build 24 houses, five build 120 houses, six
build 720 houses, and seven build 5040 houses. From there on go out and
calculate that which the mouth cannot speak and the ear cannot hear.|
(The Sefer Yezirah)
This is the earliest reference to factorials that I can find. The Sefer Yezirah (Book of Creation) is thought to have been written around the third century AD (or CE if you prefer). I would love to here of any earlier records of the use of factorials in Europe or in other cultures. I have found very little on the internet.