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%I #19 Dec 25 2021 13:35:51
%S 0,1,2,5,14,40,111,299,793,2096,5553,14758,39294,104673,278773,742197,
%T 1975582,5258269,13995810,37253664,99163215,263958623,702620141,
%U 1870267300,4978351449,13251558642,35273486910,93892303905,249926170873,665263248665,1770823721530
%N Expansion of x*(x^4 - x^3 + 4x^2 - 3x + 1)/(1 - 5x + 9x^2 - 8x^3 + 2x^4 - x^5).
%H Harvey P. Dale, <a href="/A111110/b111110.txt">Table of n, a(n) for n = 0..1000</a>
%H M. H. Albert and M. D. Atkinson, <a href="http://dx.doi.org/10.1016/j.disc.2005.06.016">Simple permutations and pattern restricted permutations</a>, Discr. Math., 300 (2005), 1-15.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,8,-2,1).
%t CoefficientList[ Series[x*(x^4 - x^3 + 4x^2 - 3x + 1)/(1 - 5x + 9x^2 - 8x^3 + 2x^4 - x^5), {x, 0, 30}], x] (* _Robert G. Wilson v_, Oct 15 2005 *)
%t LinearRecurrence[{5,-9,8,-2,1},{0,1,2,5,14,40},40] (* _Harvey P. Dale_, Dec 25 2021 *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Oct 14 2005