%I M4916 N2109 #38 Sep 08 2022 08:44:28
%S 13,192,1085,3880,10656,24626,50380,94128,163943,270004,424839,643568,
%T 944146,1347606,1878302,2564152,3436881,4532264,5890369,7555800,
%U 9577940,12011194,14915232,18355232,22402123,27132828,32630507,38984800,46292070
%N Number of discordant permutations.
%D J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H J. Riordan, <a href="/A000211/a000211.pdf">Discordant permutations</a>, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15, 20,-15,6,-1).
%F From Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001: (Start)
%F G.f.: -x^5(8x^5 - 6x^4 + 10x^3 - 128x^2 - 114x - 13) / ((1 - x)^6).
%F a(n) = 81/40n^5 - 135/4n^4 + 1719/8n^3 - 2487/4n^2 + 3463/5n, n>4. (End)
%p r := n->81/40*n^5-135/4*n^4+1719/8*n^3-2487/4*n^2+3463/5*n; seq(r(n), n=5..40); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
%p A000563:=-(-13-114*z-128*z**2+10*z**3-6*z**4+8*z**5)/(z-1)**6; # conjectured by _Simon Plouffe_ in his 1992 dissertation
%t LinearRecurrence[{6, -15, 20, -15, 6, -1}, {13, 192, 1085, 3880, 10656, 24626}, 30] (* _Jean-François Alcover_, Feb 10 2016 *)
%o (Magma) [81/40*n^5-135/4*n^4+1719/8*n^3-2487/4*n^2+3463/5*n: n in [5..45]]; // _Vincenzo Librandi_, Feb 10 2016
%K nonn,easy
%O 5,1
%A _N. J. A. Sloane_
%E More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001