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A000517
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Number of permutations of length n with exactly three valleys.
(Formerly M5431 N2360)
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6
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272, 7936, 137216, 1841152, 21253376, 222398464, 2174832640, 20261765120, 182172651520, 1594922762240, 13684856848384, 115620218667008, 965271355195392, 7984436548730880, 65569731961159680, 535438370914959360, 4353038473793372160, 35266789418949672960
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OFFSET
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7,1
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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. 261.
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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LINKS
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Index entries for linear recurrences with constant coefficients, signature (40, -700, 7056, -45360, 194304, -561728, 1082624, -1332224, 946176, -294912).
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FORMULA
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G.f.: 16x^7(17-184x+636x^2-720x^3)/((1-2x)^4*(1-4x)^3*(1-6x)^2*(1-8x)). - Ralf Stephan, Sep 18 2003 [Proved by Désiré André, 1895, p.154, for circular permutations (see A008303). Peter Luschny, Aug 07 2019]
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MATHEMATICA
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nn = 20; Drop[CoefficientList[Series[16 x^7 (17 - 184 x + 636 x^2 - 720 x^3)/((1 - 2 x)^4*(1 - 4 x)^3*(1 - 6 x)^2*(1 - 8 x)), {x, 0, nn}], x], 7] (* T. D. Noe, Jun 20 2012 *)
LinearRecurrence[{40, -700, 7056, -45360, 194304, -561728, 1082624, -1332224, 946176, -294912}, {272, 7936, 137216, 1841152, 21253376, 222398464, 2174832640, 20261765120, 182172651520, 1594922762240}, 20] (* Jean-François Alcover, Feb 09 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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