Which increases faster

1, 2^2, 3^(3^3), 4^(4^(4^4)), 5^(5^(5^(5^5))), ...

or

1, 2!, 3!!, 4(3!!)!, 5(4(3!!))!, 6(5(4(3!!)))!, ...


note on notation:  3(4)! = 3!!!!.

no one?  Well, this was so hard even the Arkansas State Math Master wasn't sure about it.

I'd say the latter one. Simply due to the fact that the factorial stuff has an enormous growth rate.

Can they be graphed by any ordinary hardware/software out there?

I'll define these as functions and run them in python interpreter, to say the 25th term. If I don't make it back my computer's crashed.

are you defining 3!! as (3!)! or the double, odd factorial function?

rewrite this problem recursively and properly using the gamma function

as I read this problem the tetration sequence clearly grows much faster. check using polynomial approximations, honestly, not even an interesting problem.

the latter one