Search: id:A000564
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%I A000564 M5099 N2208
%S A000564 20,371,2588,11097,35645,94457,218124,454220,872648,1571715,
%T A000564 2684936,4388567,6909867,10536089,15624200,22611330,32025950,44499779,
%U A000564 60780420,81744725,108412889,141963273,183747956,235309016,298395540
%N A000564 Number of discordant permutations.
%D A000564 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000564 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000564 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A000564 J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
%H A000564 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A000564 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A000564 G.f.: -x^6(2x^7-4x^6+36x^5-29x^4-72x^3-411x^2-231x-20)/((1-x)^7).
%F A000564 a(n)=81/80n^6-405/16n^5+4113/16n^4-21267/16n^3+140357/40n^2-7587/2n, 
               n>6.
%p A000564 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);
%p A000564 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 S. Plouffe in his 1992 dissertation.]
%Y A000564 Sequence in context: A115100 A049683 A014901 this_sequence A019580 A084329 
               A097832
%Y A000564 Adjacent sequences: A000561 A000562 A000563 this_sequence A000565 A000566 
               A000567
%K A000564 nonn
%O A000564 3,1
%A A000564 N. J. A. Sloane (njas(AT)research.att.com).
%E A000564 More terms, formulae and Maple code from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 
               2/17/01

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