

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}.


1



0, 4, 72, 1280, 25000, 544320, 13176688, 352321536, 10331213040, 330000000000, 11412466824440, 425000788033536, 16961005969166168, 722280443661271040, 32696077148437500000, 1567973246265311887360, 79415065141088329360992
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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^21) / 3.  Franklin T. AdamsWatters, 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^21)/3, {n, 20}] (* Harvey P. Dale, Sep 24 2011 *)


PROG

(Magma) [n^n*(n^21) / 3: n in [1..20]]; // Vincenzo Librandi, Sep 25 2011


CROSSREFS

Cf. A111873, A111874, A111903.
Sequence in context: A165212 A263219 A100521 * A060645 A203073 A231033
Adjacent sequences: A111865 A111866 A111867 * A111869 A111870 A111871


KEYWORD

easy,nonn,nice


AUTHOR

James East, Nov 23 2005


EXTENSIONS

More terms from Franklin T. AdamsWatters, Dec 14 2006


STATUS

approved



