OFFSET
1,2
LINKS
James East The Work Performed by a Transformation Semigroup, preprint 2005.
FORMULA
Sum(i, j=1...n;k, l=0...n, |i-j|*(i-1 choose k)*(j+k-1 choose k)*(n-i choose l)*(n-j+l choose l))
EXAMPLE
When n=2 there are 8 order-preserving partial maps {1,2}->{1,2}. these are (1 2), (1 1), (2 2), (1 -), (2 -), (- 1), (- 2) (- -). Adding up the work performed by these maps (from left to right as arranged above) gives a(2)=0+1+1+0+1+1+0+0=4.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
James East, Nov 23 2005
STATUS
approved