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%I #20 Sep 08 2022 08:45:44
%S 0,0,0,0,8,80,528,2912,14592,69120,316160,1413632,6223872,27103232,
%T 117067776,502456320,2145517568,9122349056,38644678656,163186343936,
%U 687144960000,2886107922432,12094385684480,50577004298240,211105074905088,879606785638400
%N Number of permutations of 1..n arranged in a circle with exactly 2 local maxima.
%H Alois P. Heinz, <a href="/A159710/b159710.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (14,-76,200,-256,128).
%F G.f.: -8*(2*x^2-4*x+1)*x^4 / ((4*x-1)^2*(2*x-1)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009
%F a(n) = 2^(-5+n)*(4+2^n-4*n)*n for n>1. - _Colin Barker_, Oct 26 2015
%t LinearRecurrence[{14,-76,200,-256,128},{0,0,0,0,8,80,528},30] (* _Harvey P. Dale_, Sep 23 2017 *)
%t Join[{0,0}, Table[2^(-5+n)*(4+2^n-4*n)*n, {n, 2, 30}]] (* _G. C. Greubel_, Jun 02 2018 *)
%o (PARI) concat([0, 0, 0, 0], Vec(-8*(2*x^2-4*x+1)*x^4 / ((4*x-1)^2*(2*x -1)^3) + O(x^100))) \\ _Altug Alkan_, Oct 26 2015
%o (PARI) a(n) = if(n==1, 0, 2^(-5+n)*(4+2^n-4*n)*n) \\ _Colin Barker_, Oct 26 2015
%o (Magma) [0,0] cat [2^(-5+n)*(4+2^n-4*n)*n: n in [2..30]]; // _G. C. Greubel_, Jun 02 2018
%Y Column k=2 of A263789.
%K nonn,easy
%O 0,5
%A _R. H. Hardin_, Apr 20 2009
%E More terms from _Alois P. Heinz_, Oct 26 2015