Mixed factorial

Mixed factorial \(n^*\)SpongeTechX, Googology World or \(M!(n)\)Mixed factorial - Tech's Large Numbers is a function recursively defined as
\[1^* = 1\]
\[(n + 1)^* = n^* +^n (n + 1)\]
where \(+^n\) is the \(n\)th hyper operator, starting at addition. For example, \(4^* = ((1 + 2) \cdot 3) \uparrow 4\). Informally, the sequence can be visualized as starting with 1 (zero zerated), adding 2, multiplying by 3, exponentiating by 4, tetrating by 5, ...
The function was coined by an author under the alias of "" (formerly SpongeTechX).
The mixed factorial also appeared on the hoax Wikipedia page for the Chihiro numbers, which referred to it as the lesser Chihiro factorial.Archived version of the Wikipedia article
== Values ==
Some examples are given below:
n	n*
1	1
2	(1+2)=3
3	(3*3)=9
4	94=6,561
5	\(^56,561=6,561\uparrow\uparrow5=6,561^{6,561^{6,561^{6,561^{6,561}}}}\)
6	(56,561)↑↑↑6
== Extension ==
By repeating the process of taking mixed factorial we get numbers of form (n*)*, ((n*)*)* etc. or, equivalently, n**, n***, n****... These can be also written as n*2, n*3, etc.
For even farther extension, we can say n*x*...x, with k x's can be written as n*(x,k). As you can see, x represents the mixed factorial numbers, and k represents the amount of them.
== Example ==
To show how this function can produce such a massive number, here is the example of the calculation of the 2 uppermost exponent of 5*, calculated using https://defuse.ca/big-number-calculator.htm and http://www.javascripter.net/math/calculators/100digitbigintcalculator.htm:
The product itself has 25,044 digits.
==Sources==
==See also==
* Factorial
Category:Factorials
Category:SpongeTechX
Category:Functions