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Search: id:A000130
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| A000130 |
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One-half the number of permutations of length n with exactly 1 rising or falling successions.
(Formerly M1528 N0598)
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+0
12
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| 0, 0, 1, 2, 5, 20, 115, 790, 6217, 55160, 545135, 5938490, 70686805, 912660508, 12702694075, 189579135710, 3019908731105, 51139445487680, 917345570926087, 17376071107513090, 346563420097249645, 7259714390232227300, 159352909727731210835, 3657569576966074846118
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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(1/2) times number of permutations of 12...n such that exactly one of the following occurs: 12, 23, ..., (n-1)n, 21, 32, ..., n(n-1).
Partial sums seem to be in A000239. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 28 2003
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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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Coefficient of t^1 in S[n](t) defined in A002464, divided by 2.
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CROSSREFS
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Cf. A002464, A086853. Equals A086852/2. A diagonal of A010028.
Adjacent sequences: A000127 A000128 A000129 this_sequence A000131 A000132 A000133
Sequence in context: A129949 A127065 A052850 this_sequence A009599 A112833 A144503
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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