The megafactorial is a factorial-based function. This function was defined by HaydenTheGoogologist2009.
Megafactorial, denoted by n‽, is defined as follows:
n‽ = a_n * a_{n - 1} * a_{n - 2} * ... * a_3 * a_2 * a_1, where n ∈ ℕ+ and a_n is the nth exponential factorial number.
In hyperfactorial array notation, this is equal to n!1 * (n - 1)!1 * (n - 2)!1 * ... * 3!1 * 2!1 * 1!1.
The approximations of the first values of the megafactorial are: (results from WolframAlpha)
1‽ = a_1 = 1
2‽ = a_2 * a_1 = 2^1 * 1 = 2 * 1 = 4
3‽ = a_3 * a_2 * a_1 = 3^2^1 * 2^1 * 1 = 9 * 2 * 1 = 18
4‽ = a_4 * a_3 * a_2 * a_1 = 4^3^2^1 * 3^2^1 * 2^1 * 1 = 262,144 * 9 * 2 * 1 = 4,718,592
5‽ = a_5 * a_4 * a_3 * a_2 * a_1 = 5^4^3^2^1 * 4^3^2^1 * 3^2^1 * 2^1 * 1 ~ 2.92839116808901729906772593950390295109293694710144327004 * 10^183237
6‽ = a_6 * a_5 * a_4 * a_3 * a_2 * a_1 = 6^5^4^3^2^1 * 5^4^3^2^1 * 4^3^2^1 * 3^2^1 * 2^1 * 1 ~ 10^10^10^5.262998202542665
7‽ = a_7 * a_6 * a_5 * a_4 * a_3 * a_2 * a_1 = 7^6^5^4^3^2^1 * 6^5^4^3^2^1 * 5^4^3^2^1 * 4^3^2^1 * 3^2^1 * 2^1 * 1 ~ 10^10^10^10^5.262998202542665
The growth rate of n‽ can be approximated as f_3(f_2(n)).