User blog comment:Googleaarex/Factorial N-ational/@comment-25371339-20140918003952/@comment-25371339-20140921132022

Extension!

n!1&2 = n!1, 1, 1, 1, 1, ...2 2 2 2 2  w/ n levels

n!2&2  = n!1, 1, 1, 1, 1, ...2 2 2 2 2  w/ n!1, 1, 1, 1, 1, ...2 2 2 2 2  w/ n levels levels

n!1,2&2 = n!n&2

And so on...

In the other hand we have:

n!1&3 = n!1, 1, 1, 1, 1, ...2 2 2 2 2 &2 w/ n levels

More coming soon!