User blog comment:Googology Noob/SuperJedi's X Function/@comment-25601061-20151229031717/@comment-27173506-20151229183846

Here's my definition of HAN up to n!m:

U(a,b,1)=a^b

U(a,1,c)=a

U(a,Sb,Sc)=U(a,U(a,b,Sc),c)

F(1,y)=1

F(Sx,y)=U(Sx,F(x,y),y)

59 symbols. The definition up to n![m] is far trickier though.