I could use some help figuring out what the next row is in the pattern below (and what the rule is generally for each number in the series). I put it in a triangle because I'm pretty sure it has something to do with Pascal's triangle. The only other thing that's clear to me is that the left side of the triangle is the factorials $2!,3!,4!$ etc., and the right side increases by multiples of $4,6,8,10$, etc.
There's also some interesting stuff going on with the digits in some of the numbers adding up to multiples of 3 (6, 9, 12, 15, etc.) but this doesn't really help in terms of figuring out the rule behind the pattern.
$\begin{array} &&&&&&&2\\ &&&&&6&&8\\ &&&&24&&72&&48\\ &&&120&&600&&864&&384\\ &&720&&5280&&12240&&11520&&3840\\ &5040&&50400&&166320&&247680&&172800&&46080\\ \end{array}$
Thanks