A111868 The work performed by a function f:{1,...,n} -> {1,...,n} is defined to be work(f) = Sum_{i=1..n} |i - f(i)|; a(n) is equal to sum(work(f)) where the sum is over all functions f:{1,...,n}->{1,...,n}.

0, 4, 72, 1280, 25000, 544320, 13176688, 352321536, 10331213040, 330000000000, 11412466824440, 425000788033536, 16961005969166168, 722280443661271040, 32696077148437500000, 1567973246265311887360, 79415065141088329360992, 4236296602773593878953984

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..300

James East, The Work Performed by a Transformation Semigroup, preprint 2005.

Formula

a(n) = n^n*(n^2-1) / 3. - Franklin T. Adams-Watters, Dec 14 2006

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.

Mathematica

Table[n^n (n^2-1)/3, {n, 20}] (* Harvey P. Dale, Sep 24 2011 *)

Prog

(Magma) [n^n*(n^2-1) / 3: n in [1..20]]; // Vincenzo Librandi, Sep 25 2011

Crossrefs

Cf. A111873, A111874, A111903.

Sequence in context: A263219 A358295 A100521 * A060645 A363987 A203073

Adjacent sequences: A111865 A111866 A111867 * A111869 A111870 A111871

Keyword

easy,nonn,nice

Author

James East, Nov 23 2005

Extensions

More terms from Franklin T. Adams-Watters, Dec 14 2006

Status

approved