In my previous blog post entitled slow growing trees I described a function called the factorial summation tree function or fst(x) for short. What this function does is it takes the sum of all the factorials from 1! to a given value x for example [fst(10)=1!+2!+3!+4!+5!+6!+7!+8!+9!+10! this comes to 4037913. This function is quite slow as you have to input some very large numbers to get a large number out. To fix that I have devised a function called fst[2](x) what this does is instead of taking the factorial of a number it takes the double factorial it also works through multiplication instead of addition. For example fst[2](5)=1!!*2!!*3!!*4!!*5!!=5.97670760389 × 10^225.See quite an improvement over the fst(x) function but still its pretty weak compared to what I have planned next because the fst[3](x)function doesn't multiply it takes the double factorial exponents or n!!^(n!!) fst[3](5)=2!!^(2!!)^3!!^(3!!)^4!!^(4!!)^5!!^(5!!)^1!!^(1!!) fst[4](x)doesn't use double factorials it uses repeated hyper factorials for we use an h to denote the hyper factorials. For example fst[4](3)=h3^(h^3^h3)^h2^(h2)^(h1)this comes to 10^2.559879934 × 10^56220. fst[4](4)=h4^(h4^h4^h4)^h3^(h3^h3)^h2^(h2)^h1 this may be quite impressive but not as impressive as fst[4](10) or h10^(h10^h10^h10^h10^h10^h10^h10^h10^h10)^h9^(h9^h9^h9^h9^h9^h9^h9^h9)^h8^(h8^h8^h8^h8^h8^h8^h8)^h7^(h7^h7^h7^h7^h7^h7)^h6^(h6^h6^h6^h6^h6)^h5^(h5^h5^h5^h5)^h4^(h4^h4^h4)^h3^(h3^h3)^h2^(h2)^h1. This is going to produce a very large number in part 2 I am going to show you the 5th part of the fst function.

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