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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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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
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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.
Sequence in context: A129949 A127065 A052850 this_sequence A009599 A112833 A144503
Adjacent sequences: A000127 A000128 A000129 this_sequence A000131 A000132 A000133
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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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