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A000562
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Number of discordant permutations.
(Formerly M4657 N1994)
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2
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9, 95, 420, 1225, 2834, 5652, 10165, 16940, 26625, 39949, 57722, 80835, 110260, 147050, 192339, 247342, 313355, 391755, 484000, 591629, 716262, 859600, 1023425, 1209600, 1420069, 1656857, 1922070, 2217895, 2546600, 2910534, 3312127, 3753890, 4238415, 4768375, 5346524, 5975697
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OFFSET
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4,1
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REFERENCES
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J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
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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FORMULA
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From Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001: (Start)
G.f.: -x^4(2x^5 - 4x^4 + 15x^3 - 35x^2 - 50x - 9) / ((1 - x)^5).
a(n) = 27/8n^4 - 135/4n^3 + 921/8n^2 - 539/4n, n>4. (End)
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MAPLE
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ff := n->27/8*n^4-135/4*n^3+921/8*n^2-539/4*n; seq(ff(n), n=5..40); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
A000562:=(-9-50*z-35*z**2+15*z**3-4*z**4+2*z**5)/(z-1)**5; # conjectured by Simon Plouffe in his 1992 dissertation
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MATHEMATICA
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Join[{9}, LinearRecurrence[{5, -10, 10, -5, 1}, {95, 420, 1225, 2834, 5652}, 40]] (* Jean-François Alcover, Feb 10 2016 *)
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PROG
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(Magma) [9] cat [27/8*n^4-135/4*n^3+921/8*n^2-539/4*n: n in [5..45]]; // Vincenzo Librandi, Feb 10 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
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STATUS
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approved
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