User:Wythagoras/Dollar function/Legion Nested Array Notation I

Legion Nested Array Notation is the seventh part of Dollar Function.

Examples
\(0,_{0,c}1 = 0,_{[0,_{[0,_{[0,_{...}1],c-1}1],c-1}1],c-1}1\)

\(a,_{0,c}1 = 0,_{[a-1,_{0,c}1][a-1,_{0,c}1],c-1}1\)

\(0,_{0,0,c}1 = 0,_{0,[0,_{0,[0,_{0,[0,_{...}1],c-1}1],c-1}1],c-1}1\)

The limit is \(0,_{0,_{0,_{...}1}1}1\)

Definition
17. \(0,_{\diamond,0,c,\bullet}1 = 0,_{\diamond,[0,_{\diamond,[0,_{\diamond,[0,_{...}1],c-1,\bullet}1],c-1,\bullet}1],c-1,\bullet}1\)

18. \(a\bullet,_{\diamond,0,c,\bullet}1 = 0,_{\diamond,[a-1\bullet,_{\diamond,0,c,\bullet}1][a-1\bullet,_{\diamond,0,c,\bullet}1],c-1,\bullet}1\)