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Hyperfactorial Array Notation

Let's start.

Note:# means rest of the array.


Rules

a![1] = a!
a![] = a
a![b] = (a![b-1])!
a![#,1] = a![#]
a![#,c,d] = a![#,a![#,c-1,d],d-1]
a![#,1,d] = a![#,a![#],d-1]

Examples

3![1] = 3! = 3*2*1 = 6
Simple.
10![1] = 10! = 10*9*8*7*6*5*4*3*2*1 = 3628800
Still simple.
3![2] = 3![1]! = 3!! = 6! = 720
Far less.
10![2] = 10![1]! = 10!! = 3628800! = 9.051994E22228103
HUGE!
3![3] = 3![2]! = 720! = 2.6012189436E1746
Still quite big.
10![3] = 10![2]! = 9.051994E22228103! = E2.012087E22228111
It's growing quickly.
Skip ahead...
10![10] = 10![9]! = EEEEEEEEE22228111.303646658
That's 9 E's! WOW!
3![2,2] = 3![3![1,2],1] = 3![3![1,2]] = 3![3![3![],1]] = 3![3![3]] = 3![2.6012189436E1746] > 10^^2.6012189436E1746
O_O
3![3,2] = 3![3![2,2],1] = 3![3![2,2]] > 3![10^^2.6012189436E1746] > 10^^10^^2.6012189436E1746
We have already reached pentational growth!
3![2,3] = 3![3![1,3],2] = 3![3![3![],2],2] = 3![3![3,2],2] > 3![10^^10^^2.6012189436E1746,2] > 10^^^10^^10^^2.6012189436E1746
@_@
3![3,3] = 3![3![2,3],2] > 3![10^^^10^^10^^2.6012189436E1746,2] > 10^^^10^^^10^^10^^2.6012189436E1746
This is hexational growth!
3![2,2,2] = 3![2,3![2,1,2],1] = 3![2,3![2,1,2] = 3![2,3![3![2],1,1]] = 3![2,3![720]] > 3![2,10^^720] > 10{10^^720}2.6012189436E1746
X_X
3![3,2,2] = 3![3,3![3,1,2],1] = 3![3,3![3,1,2] = 3![3,3![3![3],1,1]] = 3![3,3![2.6012189436E1746]] > 3![3,10^^2.6012189436E1746] > 10{10^^2.6012189436E1746}10{10^^2.6012189436E1746}2.6012189436E1746
WOAH!