- Exponential factorial
An exponential factorial is a positive integer "n" raised to the power of "n" - 1, which in turn is raised to the power of "n" - 2, and so on and so forth, that is, n^{(n - 1)^{(n - 2) dots . The exponential factorial can also be defined with the
recurrence relation a_0 = 0, a_n = n^{a_{n - 1.The first few exponential factorials are 0, 1, 2, 9,
262144 , etc. OEIS|id=A049384. So, for example, 262144 is an exponential factorial since 262144 = 4^{3^{2^{1^0}. The exponential factorials grow much more quickly than regularfactorial s or evenhyperfactorial s. The exponential factorial of 5 is 5^{262144} which is approximately 6.206069878660874 × 10183230.The sum of the reciprocals of the exponential factorials is the
irrational number 1.6111149258083767361111... OEIS2C|id=A080219.References
* Jonathan Sondow, " [http://mathworld.wolfram.com/ExponentialFactorial.html Exponential Factorial] " From
Mathworld , a Wolfram Web resource
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