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Search: id:A010028
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| A010028 |
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Triangle read by rows: T(n,k) = one-half the number of permutations of length n with exactly n-k rising or falling successions, for n >= 1, 1 <= k <= n. T(1,0) = 1 by convention. |
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9
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| 1, 1, 0, 1, 2, 0, 1, 5, 5, 1, 1, 8, 24, 20, 7, 1, 11, 60, 128, 115, 45, 1, 14, 113, 444, 835, 790, 323, 1, 17, 183, 1099, 3599, 6423, 6217, 2621, 1, 20, 270, 2224, 11060, 32484, 56410, 55160, 23811, 1, 23, 374, 3950, 27152
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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(1/2) times number of permutations of 12...n such that exactly n-k of the following occur: 12, 23, ..., (n-1)n, 21, 32, ..., n(n-1).
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REFERENCES
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F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263.
J. Riordan, A recurrence for permutations without rising or falling successions. Ann. Math. Statist. 36 (1965), 708-710.
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FORMULA
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For n>1, coefficient of t^(n-k) in S[n](t) defined in A002464, divided by 2.
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EXAMPLE
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1; 1,0; 1,2,0; 1,5,5,1; 1,8,24,20,7; ...
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CROSSREFS
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Diagonals give A001266 (and A002464), A000130, A000349, A001267, A001268.
Triangle in A086856 transposed. Cf. A001100.
Sequence in context: A086810 A085838 A094456 this_sequence A151860 A089627 A055925
Adjacent sequences: A010025 A010026 A010027 this_sequence A010029 A010030 A010031
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KEYWORD
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tabl,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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