Exponential factorial
From Wikipedia, the free encyclopedia
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, 
. The exponential factorial can also be defined with the recurrence relation 
.
The first few exponential factorials are 0, 1, 2, 9, 262144, etc. (sequence A049384 in OEIS). So, for example, 262144 is an exponential factorial since 
. The exponential factorials grow much more quickly than regular factorials or even hyperfactorials. The exponential factorial of 5 is 5262144 which is approximately 6.206069878660874 × 10183230.
The sum of the reciprocals of the exponential factorials is the irrational number 1.6111149258083767361111... A080219.
[edit] References
- Jonathan Sondow, "Exponential Factorial" From Mathworld, a Wolfram Web resource
 |
This number theory-related article is a stub. You can help Wikipedia by expanding it. |
