Exponential Factorial

Author

Eric W. Weisstein
February 6, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/ExponentialFactorial.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ExponentialFactorial.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Definition

ExpFactorial[0]:=1
ExpFactorial[n_]:=ExpFactorial[n]=n^(ExpFactorial[n-1])

Table[ExpFactorial[n],{n,0,4}]

Length[IntegerDigits[ExpFactorial[5]]]

Recurrence

v4.2

<<DiscreteMath`RSolve`

RSolve[{a[n]==n^a[n-1],a[1]==1},a[n],n]

v5.0

RSolve[{a[n]==n^a[n-1],a[1]==1},a[n],n]

Sum of reciprocals

s=Plus@@(1/Table[ExpFactorial[n],{n,5}]);//Timing

N[s,100]