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%I #14 Sep 08 2022 08:45:38
%S 0,80,1395,12560,96575,698940,4897655,33590720,226746135,1511651900,
%T 9976916015,65303466480,424472551295,2742745738460,17631936915975,
%U 112844396291840,719383026394055,4570198050070620,28944587650489535,182807922003138800,1151689908619826415
%N Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
%H Andrew Howroyd, <a href="/A151603/b151603.txt">Table of n, a(n) for n = 1..500</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-75,145,-120,36).
%F a(n) = n*((5/2)*6^n - 25*n) for n > 1. - _Andrew Howroyd_, May 04 2020
%F From _Colin Barker_, Jul 17 2020: (Start)
%F G.f.: 5*x^2*(16 + 39*x - 473*x^2 + 240*x^3 - 72*x^4) / ((1 - x)^3*(1 - 6*x)^2).
%F a(n) = 15*a(n-1) - 75*a(n-2) + 145*a(n-3) - 120*a(n-4) + 36*a(n-5) for n>5.
%F (End)
%o (Magma) [0] cat [n*((5/2)*6^n - 25*n) : n in [2..30]]; // _Wesley Ivan Hurt_, Jul 17 2020
%o (PARI) a(n) = if(n <= 1, 0, n*(5*6^n/2 - 25*n)) \\ _Andrew Howroyd_, May 04 2020
%o (PARI) Vec(5*x^2*(16 + 39*x - 473*x^2 + 240*x^3 - 72*x^4) / ((1 - x)^3*(1 - 6*x)^2) + O(x^21)) \\ _Colin Barker_, Jul 17 2020
%Y Cf. A151583.
%K nonn,easy
%O 1,2
%A _R. H. Hardin_, May 21 2009
%E Terms a(7) and beyond from _Andrew Howroyd_, May 04 2020
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