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%I #10 Jul 19 2020 09:44:23
%S 0,50,42035,22286180,10637332433,4951385566862,2291336707020095,
%T 1058974724436063848,489282897651319234589,226052182024142033107730,
%U 104436435218150212780973867,48249663449218668484434011660,22291347308935948403947280066153,10298602712004866151067473095589974
%N 1/7 of the number of permutations of 6 indistinguishable copies of 1..n with exactly 3 local maxima.
%H Andrew Howroyd, <a href="/A152514/b152514.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 (651,-98049,5130937,-81120186,508243680,-1118136096).
%F From _Colin Barker_, Jul 19 2020: (Start)
%F G.f.: x^2*(50 + 9485*x - 176155*x^2 - 6027882*x^3 - 3111696*x^4) / ((1 - 7*x)^3*(1 - 84*x)^2*(1 - 462*x)).
%F a(n) = 651*a(n-1) - 98049*a(n-2) + 5130937*a(n-3) - 81120186*a(n-4) + 0*a(n-5) - 0*a(n-6) for n>6.
%F (End)
%o (PARI) \\ PeaksBySig defined in A334774.
%o a(n) = {PeaksBySig(vector(n,i,6), [2])[1]/7} \\ _Andrew Howroyd_, May 12 2020
%o (PARI) concat(0, Vec(x^2*(50 + 9485*x - 176155*x^2 - 6027882*x^3 - 3111696*x^4) / ((1 - 7*x)^3*(1 - 84*x)^2*(1 - 462*x)) + O(x^15))) \\ _Colin Barker_, Jul 19 2020
%Y Cf. A152513, 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
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