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A001268
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One-half the number of permutations of length n with exactly 4 rising or falling successions.
(Formerly M4805 N2053)
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4
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0, 0, 0, 0, 0, 1, 11, 113, 1099, 11060, 118484, 1366134, 16970322, 226574211, 3240161105, 49453685911, 802790789101, 13815657556958, 251309386257874, 4818622686395380, 97145520138758844, 2054507019515346789, 45484006970415223287, 1052036480881734378541
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| (1/2) times number of permutations of 12...n such that exactly 4 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.
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).
J. Riordan, A recurrence for permutations without rising or falling successions. Ann. Math. Statist. 36 (1965), 708-710.
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FORMULA
| Coefficient of t^4 in S[n](t) defined in A002464, divided by 2.
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CROSSREFS
| Cf. A002464, A000130, A086852. Equals A086855/2. A diagonal of A010028.
Sequence in context: A166572 A111463 A142483 * A065538 A104096 A087391
Adjacent sequences: A001265 A001266 A001267 * A001269 A001270 A001271
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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