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1/10 of the number of permutations of 4 indistinguishable copies of 1..n with exactly 2 local maxima.
6

%I #11 Jul 16 2020 06:24:37

%S 0,3,140,5175,183000,6416875,224662500,7863609375,275228750000,

%T 9633019921875,337155773437500,11800452490234375,413015839453125000,

%U 14455554393310546875,505944403833007812500,17708054134515380859375,619781894709960937500000,21692366314858856201171875

%N 1/10 of the number of permutations of 4 indistinguishable copies of 1..n with exactly 2 local maxima.

%H Andrew Howroyd, <a href="/A152504/b152504.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (45,-375,875).

%F a(n) = (11*35^(n-1) - 11*5^(n-1) - 12*(n-1)*5^(n-1))/90. - _Andrew Howroyd_, May 10 2020

%F From _Colin Barker_, Jul 16 2020: (Start)

%F G.f.: x^2*(3 + 5*x) / ((1 - 5*x)^2*(1 - 35*x)).

%F a(n) = 45*a(n-1) - 375*a(n-2) + 875*a(n-3) for n>3.

%F (End)

%o (PARI) a(n) = {(11*35^(n-1) - 11*5^(n-1) - 12*(n-1)*5^(n-1))/90} \\ _Andrew Howroyd_, May 10 2020

%o (PARI) concat(0, Vec(x^2*(3 + 5*x) / ((1 - 5*x)^2*(1 - 35*x)) + O(x^20))) \\ _Colin Barker_, Jul 16 2020

%Y Cf. A152494, A334773.

%K nonn,easy

%O 1,2

%A _R. H. Hardin_, Dec 06 2008

%E Terms a(9) and beyond from _Andrew Howroyd_, May 10 2020