User blog comment:Googleaarex/Factorial N-ational/@comment-25371339-20140918003952/@comment-25371339-20140920130214

Continuation.

n! 1(1,3)2 ,1,2   = n!1(n,2)2 ,1,2

In fact, just re-use our old operators.

Next we have:

 n! 1,1,3   = n!(1(1(...(1(1(1(n)2)2)2)...)2)2)2,1,2  w/ n levels

n!1,1,1,2  = n!1,1,n

Same thing.

Next we have:

 n! 1,1, 1,1,2   = n!1,1, (1(1(...(1(1(1(n)2)2)2)...)2)2)2  w/ n levels

Ditto.

Next we have:

 n! 1,2,2   = n!1,1, 1,1, 1,1,..., <sub style="line-height:0px;">1,1, <sub style="line-height:0px;">1,1,2  w/ n levels

Again.

Finally:

<sub style="line-height:0px;"> n! <sub style="line-height:0px;">1,<sub style="line-height:0px;">1,1,2 ,2   = n!<sub style="line-height:0px;">1,(1(1(...(1(1(1(n)2)2)2)...)2)2)2,2  w/ n levels

etc.

The limit is n!<sub style="line-height:0px;">1,<sub style="line-height:0px;">1,<sub style="line-height:0px;">1,...,<sub style="line-height:0px;">1,1,2 ,...,2 ,2 ,2