User blog comment:QuasarBooster/Extra-Growth Hierarchy, extension of FGH/@comment-24509095-20150615174310/@comment-24923514-20150615205008

It was just the result of a couple days' contemplation. The old n+1 is a plausible start, but I thought it would leave this extension a little too closely-resembling of FGH. n! was another convincing start, but it limits outputs of 0,1,and 2 for any subscript. After conceiving a handful of functions, 2n^2 was a compromise of power and practicality, allowing higher values for 0,1,and 2 yet not exploding off-the-bat as much as n^n would.