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Search: id:A112858
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| A112858 |
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Table read by anti-diagonals: T(n,k) = count of increasing runs in strings of length n*k formed by concatenating k permutations of [n]. |
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3
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| 1, 2, 3, 3, 11, 12, 4, 32, 132, 60, 5, 84, 1152, 2664, 360, 6, 208, 9072, 93312, 80640, 2520, 7, 496, 67392, 2944512, 14169600, 3412800, 20160, 8, 1152, 482112, 87588864, 2239488000, 3608064000, 192326400, 181440, 9, 2624, 3359232, 2508226560
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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The 1st column T(n,1) is A001710(n+1), i.e. (n+1)!/2. The 2nd column T(n,2) is the outer diagonal of triangle A122823.
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FORMULA
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T(n,k) = (k(n+1)/2 - (k-1)(n-1)/2n) * (n!)^k
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EXAMPLE
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Table begins:
1 2 3 4 ...
3 11 32 84 ...
12 132 1152 9072 ...
60 2664 93312 2944512 ...
...
Example: Take the permutations of [2] namely 12 and 21 and form all possible strings that are concatenations of 2 of these permutations. These are 1212,1221,2112,2121 with 2,3,3,3 increasing runs respectively. T(2,2) = 2+3+3+3 = 11
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CROSSREFS
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Cf. A001710, A122823, A110952.
Sequence in context: A094416 A117030 A009097 this_sequence A127003 A039793 A106243
Adjacent sequences: A112855 A112856 A112857 this_sequence A112859 A112860 A112861
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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David J. Scambler (dscambler(AT)bmm.com), Nov 22 2006
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