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Search: id:A068106
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| A068106 |
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Triangle read by rows, formed by starting with factorial numbers (A000142) and repeatedly taking differences. T(n,n) = n!, T(n,k) = T(n,k+1)-T(n-1,k). |
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9
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| 1, 0, 1, 1, 1, 2, 2, 3, 4, 6, 9, 11, 14, 18, 24, 44, 53, 64, 78, 96, 120, 265, 309, 362, 426, 504, 600, 720, 1854, 2119, 2428, 2790, 3216, 3720, 4320, 5040, 14833, 16687, 18806, 21234, 24024, 27240, 30960, 35280, 40320, 133496, 148329, 165016, 183822, 205056
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Triangle T(n,k) (n>=1, 1<=k<=n) giving number of ways of winning with (n-k+1)st card in the generalized "Game of Thirteen" with n cards.
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REFERENCES
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P. R. de Montmort, On the Game of Thirteen (1713), reprinted in Annotated Readings in the History of Statistics, ed. H. A. David and A. W. F. Edwards, Springer-Verlag, 2001, pp. 25-29.
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LINKS
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D. Dumont, Matrices d'Euler-Seidel, Sem. Loth. Comb. B05c (1981) 59-78.
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FORMULA
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T(n, k) = Sum_{ j>= 0} (-1)^j*binomial(n-k, j)*(n-j)! . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), May 29 2005
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EXAMPLE
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Triangle begins
1..1..2..6..24..120..720...
...0..1..4..18..96...600...
......1..3..14..78...504...
.........2..11..64...426...
............9...53...362...
................44...309...
.....................265...
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CROSSREFS
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Row sums give A002467. Diagonals include A000166, A000255, A055790, A000142.
See A047920 for another version.
(When seen as array) Main diagonal is in A033815.
Adjacent sequences: A068103 A068104 A068105 this_sequence A068107 A068108 A068109
Sequence in context: A102543 A068598 A035561 this_sequence A005856 A107293 A107379
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KEYWORD
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nonn,easy,tabl,nice
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AUTHOR
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njas, Apr 12 2002
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 01 2003
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