User blog comment:VoidSansXD/Notation thingy/@comment-35470197-20190404222214

Good recursion! You have improved in writing definitions greatly well.

By the way, I found typos. Maybe φφ3(n) should be φφ2(φφ2(φφ2(φφ2............φφ2(φφ2(φφ2(φφ2(n)))))............. and φφx(n) should be φφ(x-1)(φφ(x-1)..............φφ(x-1)(φφ(x-1)(φφ(x-1)(n))))))..................)))). You wrote extra (n)'s.

In addition, φ2(n) is not n!. It is 0 for any n > 0 :D