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A105350
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Largest squared factorial dividing n!.
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2
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1, 1, 1, 4, 4, 36, 36, 576, 576, 518400, 518400, 518400, 518400, 25401600, 25401600, 1625702400, 1625702400, 131681894400, 131681894400, 13168189440000, 131681894, 40000, 1593350922240000, 1593350922240000, 229442532802560000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n) = A001044(A056039(n)) = A056038(n)^2.
Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 24 2008: (Start)
a(n)=number of permutations of {1,2,...,n} with no even entry followed by a smaller entry. Example: a(4)=4 because we have 1234, 1324, 3124 and 2314.
a(n)=number of permutations p of {1,2,...,n} such that p(j) is odd whenever j is even. Example: a(4)=4 because we have 4123, 2143, 2341 and 4321.
a(n)=A134434(n,0). (End)
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REFERENCES
| S. Kitaev and J. Remmel, Classifying descents according to parity, Annals of Combinatorics, 11, 2007, 173-193. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 24 2008]
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LINKS
| Index entries for sequences related to factorial numbers.
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FORMULA
| a(2n-1)=a(2n)=(n!)^2. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 24 2008]
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MAPLE
| seq(factorial(ceil((1/2)*n))^2, n = 1 .. 24); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 24 2008]
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CROSSREFS
| Cf. A000290, A000142, A055771.
A134434 [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 24 2008]
Sequence in context: A145109 A181858 A180064 * A126936 A129357 A100303
Adjacent sequences: A105347 A105348 A105349 * A105351 A105352 A105353
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 01 2005
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