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A000349
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One-half the number of permutations of length n with exactly 2 rising or falling successions.
(Formerly M3932 N1617)
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8
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0, 0, 0, 1, 5, 24, 128, 835, 6423, 56410, 554306, 6016077, 71426225, 920484892, 12793635300, 190730117959, 3035659077083, 51371100102990, 920989078354838, 17437084517068465, 347647092476801301, 7280060180210901232, 159755491837445900120, 3665942433747225901707
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| (1/2) times number of permutations of 12...n such that exactly 2 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
| Coefficient of t^2 in S[n](t) defined in A002464, divided by 2.
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CROSSREFS
| Cf. A002464, A000130, A086852. Equals A086853/2. A diagonal of A010028.
Sequence in context: A055825 A006326 A058120 * A036919 A020067 A066118
Adjacent sequences: A000346 A000347 A000348 * A000350 A000351 A000352
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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