%N Triangle of T(n,k) where T(n,k)/(n-1)! is probability of player k out of n players winning a game of "Elimination": rules are that player 1 chooses one of the others at random to be eliminated, then player 2 (or 3 if player 2 has been eliminated) chooses somebody else at random from the survivors to be eliminated next, then the next surviving player chooses and so on round the circle until all but one have been eliminated.
%H <a href="http://groups.google.com/groups?threadm=3d0045e6.72372%40News.CIS.DFN.DE">alt.math.recreational discussion</a>
%F T(1, 1)=1; T(n, 1)=(n-1)*T(n-1, n-1) for n>1; T(n, 0)=0; T(n, k)=(k-2)*T(n-1, k-2)+(n-k)*T(n-1, k-1) for 1<k<=n.
%e Rows start: 1; 1,0; 0,1,1; 3,0,1,2; 8,9,3,1,3; 15,32,35,24,10,4; etc. T(4,2)=0 since if there are 4 players, there will be three eliminations and player 2 cannot make the third choice (instead either being eliminated on the first choice, or making the second choice and then being eliminated on the third choice).
%Y Row sums (i.e. denominators) are A000142 offset.
%A _Henry Bottomley_, Jun 07 2002