A111873 The work performed by a partial function f:{1,...,n}->{1,...,n} is defined to be work(f)=sum(|i-f(i)|,i in dom(f)); a(n) is equal to sum(work(f)) where the sum is over all partial functions f:{1,...,n}->{1,...,n}.

0, 6, 128, 2500, 51840, 1176490, 29360128, 803538792, 24000000000, 778122738030, 27243640258560, 1025115745389164, 41273168209215488, 1771037512207031250, 80704505322479288320, 3892895350053349478480, 198189314749641818898432

Offset

1,2

Comments

If n == -1 (mod 10^k) then 10^(n*k) divides a(n), so 10^9 divides a(9), 10^19 divides a(19),...,10^198 divides a(99), etc. - Farideh Firoozbakht, Nov 27 2005

Links

Table of n, a(n) for n=1..17.

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

Formula

(n+1)^n*(n^2-n)/3

Example

When n=2 there are 9 partial maps {1,2}->{1,2}: these are (1 1), (2 2), (1 2), (2 1), (1 -), (2 -), (- 1), (- 2) (- -). Adding up the work performed by these maps (from left to right as arranged above) gives a(2)=1+1+0+2+0+1+1+0+0=6.

Mathematica

Table[(n + 1)^n*(n^2 - n)/3, {n, 17}] (* Robert G. Wilson v *)

Crossrefs

Cf. A111867, A111874, A111903.

Sequence in context: A324093 A177756 A089314 * A348796 A012842 A012638

Adjacent sequences: A111870 A111871 A111872 * A111874 A111875 A111876

Keyword

easy,nonn

Author

James East, Nov 23 2005

Extensions

More terms from Farideh Firoozbakht and Robert G. Wilson v, Nov 27 2005

Status

approved