%I #17 Oct 21 2017 22:02:52
%S 1,1,2,6,24,88,303,1033,3544,12220,42164,145364,500954,1726408,
%T 5950050,20507364,70680192,243602952,839588620,2893682172,9973219220,
%U 34373198420,118468937648,408309065104,1407257423576,4850182474912
%N Number of permutations of length n sortable by 3 passes through a pop-stack.
%H Bjarki Ágúst Guðmundsson, <a href="/A293774/b293774.txt">Table of n, a(n) for n = 0..1000</a>
%H Anders Claesson, Bjarki Ágúst Guðmundsson, <a href="https://arxiv.org/abs/1710.04978">Enumerating permutations sortable by k passes through a pop-stack</a>, arXiv:1710.04978 [math.CO], 2017.
%F G.f.: (2*x^10 + 4*x^9 + 2*x^8 + 5*x^7 + 11*x^6 + 8*x^5 + 6*x^4 + 6*x^3 + 2*x^2 + x - 1) / (4*x^10 + 8*x^9 + 4*x^8 + 10*x^7 + 22*x^6 + 16*x^5 + 8*x^4 + 6*x^3 + 2*x^2 + 2*x - 1).
%o (PARI) Vec((2*x^10 + 4*x^9 + 2*x^8 + 5*x^7 + 11*x^6 + 8*x^5 + 6*x^4 + 6*x^3 + 2*x^2 + x - 1)/(4*x^10 + 8*x^9 + 4*x^8 + 10*x^7 + 22*x^6 + 16*x^5 + 8*x^4 + 6*x^3 + 2*x^2 + 2*x - 1) + O(x^30))
%Y Cf. A224232, A293775, A293776, A293784.
%K nonn,easy
%O 0,3
%A _Bjarki Ágúst Guðmundsson_, Oct 16 2017
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