A159737 - OEIS

%I #12 Jul 18 2020 10:03:40

%S 150,22680,2596608,273322980,27558217008,2700777267972,

%T 259275295383552,24501521550788100,2286808732032093360,

%U 211301127303186249252,19362866942233277773632,1762020891775616889450852,159395120671659354639719856,14345560860451487040265198020

%N Number of permutations of 6 indistinguishable copies of 1..n arranged in a circle with exactly 2 local maxima.

%H Andrew Howroyd, <a href="/A159737/b159737.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 (189,-10731,173215,-1094856,2420208).

%F a(n) = 3*n*(61^2*84^(n-2) + 96*7^(n-2) - 396*n*7^(n-2))/121. - _Andrew Howroyd_, May 10 2020

%F From _Colin Barker_, Jul 18 2020: (Start)

%F G.f.: 6*x^2*(5 + 7*x)*(5 - 196*x - 2401*x^2 + 2058*x^3) / ((1 - 7*x)^3*(1 - 84*x)^2).

%F a(n) = 189*a(n-1) - 10731*a(n-2) + 173215*a(n-3) - 1094856*a(n-4) + 2420208*a(n-5) for n>6.

%F (End)

%o (PARI) a(n) = {3*n*(61^2*84^(n-2) + 96*7^(n-2) - 396*n*7^(n-2))/121} \\ _Andrew Howroyd_, May 10 2020

%o (PARI) Vec(6*x^2*(5 + 7*x)*(5 - 196*x - 2401*x^2 + 2058*x^3) / ((1 - 7*x)^3*(1 - 84*x)^2) + O(x^40)) \\ _Colin Barker_, Jul 18 2020

%Y Column k=6 of A334772.

%Y Cf. A159716.

%K nonn,easy

%O 2,1

%A _R. H. Hardin_, Apr 20 2009

%E Terms a(7) and beyond from _Andrew Howroyd_, May 09 2020