A071818 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.

1, 1, 0, 0, 1, 1, 3, 0, 1, 2, 8, 9, 3, 1, 3, 15, 32, 35, 24, 10, 4, 24, 75, 143, 169, 153, 106, 50, 350, 144, 399, 722, 936, 982, 871, 636, 5088, 2450, 1214, 2283, 4085, 5696, 6644, 6763, 6097, 54873, 40704, 22238, 12184, 15057, 25472, 37513, 47464, 53271, 54104

Offset

1,7

Links

Table of n, a(n) for n=1..55.

alt.math.recreational discussion

Formula

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.

Example

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).

Crossrefs

Row sums (i.e. denominators) are A000142 offset.

Sequence in context: A125209 A356517 A263313 * A014513 A144388 A133513

Adjacent sequences: A071815 A071816 A071817 * A071819 A071820 A071821

Keyword

nonn,tabl

Author

Henry Bottomley, Jun 07 2002

Status

approved