User blog:Primussupremus/Factorial summation tree function

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)=1!!^(1!!)^2!!^(2!!)^3!!^(3!!)^4!!^(4!!)^5!!^(5!!).