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%I #12 May 19 2020 14:36:57
%S 2,66,1168,16220,202416,2395540,27517568,310123764,3447919120,
%T 37934904788,413863668480,4483624403284,48285543009872,
%U 517346347249140,5518365322864384,58632646191319220,620816303380261392,6553061146974071956,68979591578665208960,724285713430953995412
%N Number of permutations of 2 indistinguishable copies of 1..n arranged in a circle with exactly 2 local maxima.
%H Andrew Howroyd, <a href="/A159716/b159716.txt">Table of n, a(n) for n = 2..200</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (29,-307,1467,-3240,2700).
%F a(n) = n*(169*10^(n-2) + 48*3^(n-2) - 84*n*3^(n-2))/49. - _Andrew Howroyd_, May 10 2020
%F From _Colin Barker_, May 19 2020: (Start)
%F G.f.: 2*x*(1 + 3*x)*(1 + x - 69*x^2 + 45*x^3) / ((1 - 3*x)^3*(1 - 10*x)^2).
%F a(n) = 29*a(n-1) - 307*a(n-2) + 1467*a(n-3) - 3240*a(n-4) + 2700*a(n-5) for n>6.
%F (End)
%o (PARI) a(n) = {n*(169*10^(n-2) + 48*3^(n-2) - 84*n*3^(n-2))/49} \\ _Andrew Howroyd_, May 10 2020
%o (PARI) Vec(2*x*(1 + 3*x)*(1 + x - 69*x^2 + 45*x^3) / ((1 - 3*x)^3*(1 - 10*x)^2) + O(x^20)) \\ _Colin Barker_, May 19 2020
%Y Column k=2 of A334772.
%K nonn,easy
%O 2,1
%A _R. H. Hardin_, Apr 20 2009
%E Terms a(11) and beyond from _Andrew Howroyd_, May 09 2020
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