User blog comment:DrCeasium/Hyperfactorial array notation: Analysis part 2/@comment-7484840-20130530171941/@comment-7484840-20130531161104

Yes, the @3 was a mistake (its been added in now). If there are no arrays with the non-1 before the (k+1) separator, then the third paragraph does not require all of the w(k)/[q@]@2]@ to exist and therefore this will resolve that problem (the italics were a bit unclear).

By when the brackets are nested, I mean that when the rules not referring to w/ operators are used on @4, when it is required by these rules to replace one of the entries in itself by the entire array, it does not just use itself, but all of the w/ chain afterwards as well.

(adding in the n!) 3![1]w/[1,1,2] = 3![1]w/[1,3] = 3![1]w/[3,2] = 3![1,1,1,2]w/[1,2] = 3![1,1,[1]w/[1,2]]w/[1,2] = 3![1,1,[1]w/[3]]w/[1,2] = 3![1,1,[1,1,1,2]w/[1]]w/[1,2] = 3![1,1,[1,1,[1]w/[1]]w/[1]]w/[1,2] = 3![1,1,[1,1,[1]w/3]w/[1]]w/[1,2] = 3![1,1,[1,1,[1,1,1,2]]w/[1]]w/[1,2] = 3![1,1,[1,1,[1,1,3]]w/[1]]w/[1,2] etc.