The exponential factorial is defined by the recurrence relation
(1)
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where . The first few terms are therefore
(2)
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(3)
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(4)
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(5)
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... (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)
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(OEIS A080219). This sum is a Liouville number and is therefore transcendental.