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Search: id:A111868
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| A111868 |
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The work performed by a function f:{1,...,n} -> {1,...,n} is defined to be work(f)=sum(|i-f(i)|,i=1...n); a(n) is equal to sum(work(f)) where the sum is over all functions f:{1,...,n}->{1,...,n}. |
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+0
1
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| 0, 4, 72, 1280, 25000, 544320, 13176688, 352321536, 10331213040, 330000000000, 11412466824440, 425000788033536, 16961005969166168, 722280443661271040, 32696077148437500000, 1567973246265311887360, 79415065141088329360992
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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James East The Work Performed by a Transformation Semigroup, preprint 2005.
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FORMULA
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a(n) = n^n (n^2-1) / 3. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 14 2006
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EXAMPLE
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When n=2 there are 4 maps {1,2}->{1,2}. these are (1 1), (2 2), (1 2), (2 1), where we show the map f:{1,2}->{1,2} as (f(1) f(2)). Adding up the work performed by these maps (from left to right as arranged above) gives a(2)=1+1+0+2=4.
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CROSSREFS
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Cf. A111873, A111874, A111903.
Sequence in context: A066992 A165212 A100521 this_sequence A060645 A003718 A012947
Adjacent sequences: A111865 A111866 A111867 this_sequence A111869 A111870 A111871
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KEYWORD
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easy,nonn,nice
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AUTHOR
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James East (jameseastseq(AT)hotmail.com), Nov 23 2005
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EXTENSIONS
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More terms from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 14 2006
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