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A001925 From rook polynomials.

%I A001925 M4151 N1724 #33 Apr 13 2022 13:25:16
%S A001925 1,6,22,64,162,374,809,1668,3316,6408,12108,22468,41081,74202,132666,
%T A001925 235160,413790,723530,1258225,2177640,3753096,6444336,11028792,
%U A001925 18818664,32024977,54367374,92094334,155688208,262711866,442556798,744355673,1250157228
%N A001925 From rook polynomials.
%D A001925 J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
%D A001925 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001925 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001925 T. D. Noe, <a href="/A001925/b001925.txt">Table of n, a(n) for n = 0..1000</a>
%H A001925 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 A001925 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A001925 J. Riordan, <a href="/A000211/a000211.pdf">Discordant permutations</a>, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
%H A001925 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,2,6,-4,-1,1).
%F A001925 Riordan gives the g.f. (1+x)/[(1-x-x^2)^2*(1-x)^3].
%p A001925 A001925:=-(1+z)/(z**2+z-1)**2/(z-1)**3; # conjectured by _Simon Plouffe_ in his 1992 dissertation
%t A001925 nn = 40; CoefficientList[Series[(1 + x)/((1 - x - x^2)^2*(1 - x)^3), {x, 0, nn}], x] (* _T. D. Noe_, Aug 17 2012 *)
%t A001925 LinearRecurrence[{5,-8,2,6,-4,-1,1},{1,6,22,64,162,374,809},40] (* _Harvey P. Dale_, Oct 15 2021 *)
%Y A001925 Cf. A002940.
%K A001925 nonn
%O A001925 0,2
%A A001925 _N. J. A. Sloane_