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A000562 Number of discordant permutations.
(Formerly M4657 N1994)
2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

REFERENCES

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).

LINKS

Table of n, a(n) for n=4..39.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]

Index entries for linear recurrences with constant coefficients, signature (5,-10, 10,-5,1).

FORMULA

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)

MAPLE

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

MATHEMATICA

Join[{9}, LinearRecurrence[{5, -10, 10, -5, 1}, {95, 420, 1225, 2834, 5652}, 40]] (* Jean-François Alcover, Feb 10 2016 *)

PROG

(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

CROSSREFS

Sequence in context: A099297 A057782 A115071 * A193216 A213019 A098450

Adjacent sequences:  A000559 A000560 A000561 * A000563 A000564 A000565

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

STATUS

approved

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Last modified July 23 22:49 EDT 2019. Contains 325278 sequences. (Running on oeis4.)