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Search: id:A047920
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| A047920 |
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Triangular array formed from successive differences of factorial numbers. |
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11
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| 1, 1, 0, 2, 1, 1, 6, 4, 3, 2, 24, 18, 14, 11, 9, 120, 96, 78, 64, 53, 44, 720, 600, 504, 426, 362, 309, 265, 5040, 4320, 3720, 3216, 2790, 2428, 2119, 1854, 40320, 35280, 30960, 27240, 24024, 21234, 18806, 16687, 14833, 362880, 322560
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Number of permutations of 1,2,...,k,n+1,n+2,...,2n-k that have no agreements with 1,...,n. For example consider 1234 and 1256, then n=4 and k=2, so T(4,2)=14. Compare A000255 for the case k=1. - Jon Perry (perry(AT)globalnet.co.uk), Jan 23 2004
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REFERENCES
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J. D. H. Dickson, Discussion of two double series arising from the number of terms in determinants of certain forms, Proc. London Math. Soc., 10 (1879), 120-122.
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LINKS
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Index entries for sequences related to factorial numbers
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FORMULA
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t(n, k) =t(n, k-1)-t(n-1, k-1) =t(n, k+1)-t(n-1, k) =n*t(n-1, k)+k*t(n-2, k-1) =(n-1)*t(n-1, k-1)+(k-1)*t(n-2, k-2) =A060475(n, k)*(n-k)! - Henry Bottomley (se16(AT)btinternet.com), Mar 16 2001
T(n, k) = Sum_{ j>= 0} (-1)^j * binomial(k, j)*(n-j)! . - Philippe DELEHAM, May 29 2005
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EXAMPLE
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1; 1,0; 2,1,1; 6,4,3,2; 24,18,14,11,9; 120,96,78,64,53,44; ...
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CROSSREFS
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Columns give A000142, A001563, A001564, etc. Cf. A047922.
See A068106 for another version of this triangle.
Orthogonal columns: A000166, A000255, A055790. Main diagonal A033815.
Adjacent sequences: A047917 A047918 A047919 this_sequence A047921 A047922 A047923
Sequence in context: A120258 A103880 A135899 this_sequence A075798 A009963 A008300
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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njas
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