n!0 = n!

n!1 = (((...(((n!)!)!)...)!)!)!)! with n levels

n!(m+1) = (((...(((n!m)!m)!m)...)!m)!m)!m)!m with n levels

n![0] = n!

n![1] = n!n

n![1]0 = n![1]

n![1](m+1) = (((...(((n![1]m)![1]m)![1]m)...)![1]m)![1]m)![1]m)![1]m with n levels

n![1][1] = n![1]n

n![2] = n![1][1][1]...[1][1][1] with n [1]'s

n![m+1] = n![m][m][m]...[m][m][m] with n [m]'s

n![0,1] = n![n]


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