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Factorial indicator!
Also I've found two interesting but basic patterns between doublings and squares!
The ratio between a doubling and a square seems to always be half of the base number, so basically:
x2 / 2x = x/2
And to use an example... Let's use 5 as the base number.
5*2 = 10 and 52 = 25
25 / 10 = 2.5
The ratio is 2.5 which is indeed the half of 5.
Also a fairly useless formula to calculate the square from the doubling is this one:
x2 / 4
And an example, using 5 as the base number again.
102 / 4 = 25
...
Note that this only really applies where X > 0 as negative numbers behave bit differently.