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A071818
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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.
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0
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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LINKS
| alt.math.recreational discussion
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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.
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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).
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CROSSREFS
| Row sums (i.e. denominators) are A000142 offset.
Sequence in context: A014573 A067166 A125209 * A014513 A144388 A133513
Adjacent sequences: A071815 A071816 A071817 * A071819 A071820 A071821
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 07 2002
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