exponential factorial

Given a positive integer n, the ”power tower” n(n-1)(n-2) is the exponential factorial of n. The recurrence relation is a1=1, an=nan-1 for n>1.

So for example, 9=321, 262144=4321. The exponential factorial for 5 has almost two hundred thousand base 10 digits. The ones that are small enough are listed in sequenceMathworldPlanetmath A049384 of Sloane’s OEIS.

The sum of the reciprocals of the exponential factorials is a Liouville numberMathworldPlanetmath.

Title exponential factorial
Canonical name ExponentialFactorial
Date of creation 2013-03-22 16:01:38
Last modified on 2013-03-22 16:01:38
Owner CompositeFan (12809)
Last modified by CompositeFan (12809)
Numerical id 7
Author CompositeFan (12809)
Entry type Definition
Classification msc 05A10
Related topic FactorialMathworldPlanetmath