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Search: id:A079402
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| A079402 |
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((n^2)!*product_{k=0..n-1} k!/(n+k)!)^2 |
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+0
2
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| 1, 1, 4, 1764, 577152576, 491609948246960400, 2794390432234620616607526201600, 225695005480541203944756162668572542540719673600
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Conjecture: this is equal to the number of permutations of n^2 distinct integers free of any monotonic increasing or decreasing (n+1)-subsequence. (By the Erdos-Szekeres Theorem, every permutation of n^2+1 distinct integers has such a subsequence.) - Joseph S. Myers (jsm(AT)polyomino.org.uk), Jan 04 2003
Claude Lenormand (claude.lenormand(AT)free.fr) confirms that this conjecture. - Jan 06, 2002.
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REFERENCES
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Martin Gardner, Riddles of The Sphinx, MAA, NML vol. 32, 1987, p. 6.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World Of Mathematics
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EXAMPLE
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The case n=2: only a(2)=4 of the 24 permutations of {1,2,3,4} are devoid of any 3-term increasing or decreasing subsequence, namely {2,1,4,3}, {2,4,1,3}, {3,1,4,2}, {3,4,1,2}.
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CROSSREFS
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a(n) = (A067700(n)/2)^2.
Sequence in context: A094546 A030253 A141090 this_sequence A024060 A004815 A062407
Adjacent sequences: A079399 A079400 A079401 this_sequence A079403 A079404 A079405
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KEYWORD
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nonn,easy
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AUTHOR
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Dean Hickerson (dean(AT)math.ucdavis.edu), Jan 06 2003
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