I'm trying to figure out the rule that's producing the series below. The first column is the factorials $1!,2!,3!,4!,5!,6!$ But I can't figure out what else is going on. So I know the next row will start with $7!=5040$, but can't say much beyond that. If someone has insight as to what the next numbers in the series are that would be much appreciated.
$1$
$2\qquad2$
$6\qquad12\qquad6$
$24\qquad72\qquad72\qquad24$
$120\qquad480\qquad720\qquad480\qquad120$
$720\qquad3600\qquad7200\qquad7200\qquad3600\qquad720$
Thanks