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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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1
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0, 4, 72, 1280, 25000, 544320, 13176688, 352321536, 10331213040, 330000000000, 11412466824440, 425000788033536, 16961005969166168, 722280443661271040, 32696077148437500000, 1567973246265311887360, 79415065141088329360992
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..300
James East The Work Performed by a Transformation Semigroup, preprint 2005.
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FORMULA
| a(n) = n^n*(n^2-1) / 3. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 14 2006
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EXAMPLE
| 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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MATHEMATICA
| Table[n^n (n^2-1)/3, {n, 20}] (* From Harvey P. Dale, Sep 24 2011 *)
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PROG
| (MAGMA) [n^n*(n^2-1) / 3: n in [1..20]]; // Vincenzo Librandi, Sep 25 2011
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CROSSREFS
| Cf. A111873, A111874, A111903.
Sequence in context: A066992 A165212 A100521 * A060645 A203073 A201976
Adjacent sequences: A111865 A111866 A111867 * A111869 A111870 A111871
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KEYWORD
| easy,nonn,nice
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AUTHOR
| James East (jameseastseq(AT)hotmail.com), Nov 23 2005
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EXTENSIONS
| More terms from Franklin T. Adams-Watters, Dec 14 2006
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