OFFSET
1,2
LINKS
James East The Work Performed by a Transformation Semigroup, preprint 2005.
FORMULA
((n^3-n)/3)*sum(i=0...n-1, (n-1 choose i)^2*i!)
EXAMPLE
When n=2 there are 7 injective partial maps {1,2}->{1,2}. these are (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)=0+2+0+1+1+0+0=4.
MATHEMATICA
f[n_] := (n^3 - n)Sum[Binomial[n - 1, k]^2*k!, {k, 0, n - 1}]/3; Array[f, 17] (* Robert G. Wilson v *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
James East, Nov 23 2005
EXTENSIONS
More terms from Robert G. Wilson v, Nov 26 2005
STATUS
approved