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%I #22 Dec 11 2020 06:09:30
%S 1,1,2,6,24,60,150,399,1145,3132,8420,22716,62128,169536,460885,
%T 1251777,3406238,9272354,25229036,68622196,186682470,507925571,
%U 1381929921,3759616968,10228269080,27827267544,75707898304,205971928848,560368255081,1524544463441
%N Number of permutations of [n] such that for each cycle c the smallest integer interval containing all elements of c has at most four elements.
%C a(n) is the number of permutations of length n avoiding the partially ordered pattern (POP) {1>5} of length 5. That is, the number of length n permutations having no subsequences of length 5 in which the first element is larger than the fifth element. - _Sergey Kitaev_, Dec 11 2020
%H Alois P. Heinz, <a href="/A276838/b276838.txt">Table of n, a(n) for n = 0..1000</a>
%H Alice L. L. Gao, Sergey Kitaev, <a href="https://arxiv.org/abs/1903.08946">On partially ordered patterns of length 4 and 5 in permutations</a>, arXiv:1903.08946 [math.CO], 2019.
%H Alice L. L. Gao, Sergey Kitaev, <a href="https://doi.org/10.37236/8605">On partially ordered patterns of length 4 and 5 in permutations</a>, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,2,12,8,-2,-5,-1).
%F G.f.: -(x-1)*(x+1)/(x^8+5*x^7+2*x^6-8*x^5-12*x^4-2*x^3-2*x^2-x+1).
%t CoefficientList[Series[-(x - 1) (x + 1)/(x^8 + 5 x^7 + 2 x^6 - 8 x^5 - 12 x^4 - 2 x^3 - 2 x^2 - x + 1), {x, 0, 29}], x] (* _Michael De Vlieger_, Oct 14 2017 *)
%Y Column k=4 of A276837.
%Y Cf. A276720.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Sep 20 2016
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