Aside from problems such as the halting problem, which aren't computable, are there any useful problems in computer science that can only be solved in time $O(2^{2^n})$, or in time $O((n!)!)$? I've heard of many difficult problems which require O(2^n) algorithms, but none that have required running times worse than that... are there any of that sort?
Highest useful complexity class
algorithms;complexity theory;time complexity