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 A000564 Number of discordant permutations. (Formerly M5099 N2208) 2
 20, 371, 2588, 11097, 35645, 94457, 218124, 454220, 872648, 1571715, 2684936, 4388567, 6909867, 10536089, 15624200, 22611330, 32025950, 44499779, 60780420, 81744725, 108412889, 141963273, 183747956, 235309016, 298395540 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,1 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 Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy] Index entries for linear recurrences with constant coefficients, signature (7,-21, 35,-35,21,-7,1). FORMULA From Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001: (Start) G.f.: -x^6(2x^7 - 4x^6 + 36x^5 - 29x^4 - 72x^3 - 411x^2 - 231x - 20) / ((1 - x)^7). a(n) = 81/80n^6 - 405/16n^5 + 4113/16n^4 - 21267/16n^3 + 140357/40n^2 - 7587/2n, n>6. (End) MAPLE rr := n - >81/80*n^6 - 405/16*n^5 + 4113/16*n^4 - 21267/16*n^3 + 140357/40*n^2 - 7587/2*n; seq(rr(n), n=7..40); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001 A000564:=(-20-231*z-411*z**2-72*z**3-29*z**4+36*z**5-4*z**6+2*z**7)/(z-1)**7; # conjectured by Simon Plouffe in his 1992 dissertation MATHEMATICA Join[{20}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {371, 2588, 11097, 35645, 94457, 218124, 454220}, 30]] (* Jean-François Alcover, Feb 10 2016 *) PROG (MAGMA) [20] cat [81/80*n^6-405/16*n^5+4113/16*n^4-21267/16*n^3+140357/40*n^2 - 7587/2*n: n in [7..45]]; // Vincenzo Librandi, Feb 10 2016 CROSSREFS Sequence in context: A228330 A014901 A290581 * A178352 A266736 A019580 Adjacent sequences:  A000561 A000562 A000563 * A000565 A000566 A000567 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001 STATUS approved

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Last modified April 21 17:29 EDT 2021. Contains 343156 sequences. (Running on oeis4.)