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Date: 16-11-2020
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Date: 30-6-2020
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Date: 5-2-2016
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The exponential factorial is defined by the recurrence relation
(1) |
where . The first few terms are therefore
(2) |
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(3) |
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(4) |
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(5) |
... (OEIS A049384). The term has digits.
The exponential factorial is therefore a kind of "factorial power tower."
The sum of the reciprocals of the exponential factorials is given by
(6) |
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(7) |
(OEIS A080219). This sum is a Liouville number and is therefore transcendental.
REFERENCES:
Sloane, N. J. A. Sequences A049384 and A080219 in "The On-Line Encyclopedia of Integer Sequences."
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