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alternating factorial
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(Definition)
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The alternating factorial  of a positive integer  is the sum
which can also be expressed with the recurrence relation
 with starting condition  . The notation n¡! (alternating an inverted exclamation mark with a regular exclamation mark) has been proposed by analogy to that of the double factorial, but has not gained much support, in part because of TeX's lack of support for Spanish characters.
The first few alternating factorials, listed in A005165 of Sloane's OEIS, are 1, 5, 19, 101, 619, 4421.
In 1999, Miodrag Zivković proved that
 and that the set of alternating factorials that are prime numbers is finite.  is the largest such known prime.
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"alternating factorial" is owned by PrimeFan. [ full author list (2) | owner history (1) ]
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(view preamble)
Cross-references: finite, prime numbers, OEIS, characters, support, double factorial, regular, alternating, recurrence relation, sum, integer, positive
There is 1 reference to this entry.
This is version 4 of alternating factorial, born on 2006-10-17, modified 2008-06-18.
Object id is 8463, canonical name is AlternatingFactorial.
Accessed 792 times total.
Classification:
| AMS MSC: | 05A10 (Combinatorics :: Enumerative combinatorics :: Factorials, binomial coefficients, combinatorial functions) |
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Pending Errata and Addenda
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