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1/60 of the number of permutations of 5 indistinguishable copies of 1..n with exactly 3 local maxima.
1

%I #11 Mar 14 2022 12:58:22

%S 0,2,1066,328314,87554515,22414176982,5672480870616,1431066048773744,

%T 360732335571459920,90911141639422741152,22910020941551289849856,

%U 5773350885207751422091264,1454885995214232796339050240,366631366567387199476086758912,92391110171365499708617443239936

%N 1/60 of the number of permutations of 5 indistinguishable copies of 1..n with exactly 3 local maxima.

%H Andrew Howroyd, <a href="/A152510/b152510.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (382,-38020,1394280,-17690400,92123136,-170698752).

%F From _Colin Barker_, Jul 19 2020: (Start)

%F G.f.: x^2*(2 + 302*x - 2858*x^2 - 120673*x^3 - 71148*x^4) / ((1 - 6*x)^3*(1 - 56*x)^2*(1 - 252*x)).

%F a(n) = 382*a(n-1) - 38020*a(n-2) + 1394280*a(n-3) - 17690400*a(n-4) + 92123136*a(n-5) - 170698752*a(n-6) for n>6.

%F (End)

%t LinearRecurrence[{382,-38020,1394280,-17690400,92123136,-170698752},{0,2,1066,328314,87554515,22414176982},20] (* _Harvey P. Dale_, Mar 14 2022 *)

%o (PARI) \\ PeaksBySig defined in A334774.

%o a(n) = {PeaksBySig(vector(n,i,5), [2])[1]/60} \\ _Andrew Howroyd_, May 12 2020

%o (PARI) concat(0, Vec(x^2*(2 + 302*x - 2858*x^2 - 120673*x^3 - 71148*x^4) / ((1 - 6*x)^3*(1 - 56*x)^2*(1 - 252*x)) + O(x^20))) \\ _Colin Barker_, Jul 19 2020

%Y Cf. A152509, A334774.

%K nonn,easy

%O 1,2

%A _R. H. Hardin_, Dec 06 2008

%E Terms a(7) and beyond from _Andrew Howroyd_, May 12 2020