User blog comment:Wythagoras/Dollars Function/@comment-5029411-20130729184030

We have a$[0(@+1)->@+1@] = a$[0(@)->{0}& {0}&... {0}& {0}&11 ...1 1 (@+1)->@@] (a &'s), a$[0(@)->0@] = [0 @] and a$[0(0)->@@] = [0->@@]

a$[0(1),1] = a$[0->{0}&... {0}&1...1 1] (a &'s)

a$[0(1)->@+11] = a$[0->{0}&... {0}&1...1 (1)->@1] (a &'s)

a$[0(@+1),1] = a$[0(@)->{0}&... {0}&1...1 1] (a &'s)

a$[0(@+1)->@+11] = a$[0(@)->{0}&... {0}&1...1 (@+1)->@1] (a &'s)