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A001266
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One-half the number of permutations of length n without rising or falling successions.
(Formerly M4426 N1871)
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4
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0, 0, 1, 7, 45, 323, 2621, 23811, 239653, 2648395, 31889517, 415641779, 5830753109, 87601592187, 1403439027805, 23883728565283, 430284458893701, 8181419271349931, 163730286973255373, 3440164703027845395, 75718273707281368117, 1742211593431076483419
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,4
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COMMENTS
| (1/2) times number of permutations of 12...n such that none of the following occur: 12, 23, ..., (n-1)n, 21, 32, ..., n(n-1).
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REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| (1/2) times coefficient of t^0 in S[n](t) defined in A002464.
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CROSSREFS
| Sequence A002464 divided by 2 for n >= 2. A diagonal of A010028.
Sequence in context: A103719 A134437 A018927 * A071971 A006680 A197796
Adjacent sequences: A001263 A001264 A001265 * A001267 A001268 A001269
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/16/01
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