cp's OEIS Frontend

A293775 Number of permutations of length n sortable by 4 passes through a pop-stack.

%I A293775 #18 Apr 17 2022 22:53:49
%S A293775 1,1,2,6,24,120,565,2473,10468,44148,187363,799605,3418967,14615713,
%T A293775 62439735,266643093,1138577340,4862025964,20763336212,88672294260,
%U A293775 378685960241,1617214869969,6906440938924,29494450730730,125958207787945,537914052728909
%N A293775 Number of permutations of length n sortable by 4 passes through a pop-stack.
%H A293775 Bjarki Ágúst Guðmundsson, <a href="/A293775/b293775.txt">Table of n, a(n) for n = 0..1000</a>
%H A293775 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 A293775 G.f.: (64*x^25 + 448*x^24 + 1184*x^23 + 1784*x^22 + 2028*x^21 + 1948*x^20 + 1080*x^19 + 104*x^18 - 180*x^17 + 540*x^16 + 1156*x^15 + 696*x^14 + 252*x^13 + 238*x^12 + 188*x^11 + 502*x^10 + 806*x^9 + 544*x^8 + 263*x^7 + 185*x^6 + 99*x^5 + 33*x^4 + 13*x^3 + 3*x^2 + x - 1) / (128*x^25 + 896*x^24 + 2368*x^23 + 3568*x^22 + 3928*x^21 + 3064*x^20 + 176*x^19 - 2304*x^18 - 2664*x^17 - 1580*x^16 - 352*x^15 - 576*x^14 - 1104*x^13 - 760*x^12 - 138*x^11 + 686*x^10 + 1238*x^9 + 869*x^8 + 382*x^7 + 210*x^6 + 102*x^5 + 27*x^4 + 12*x^3 + 3*x^2 + 2*x - 1).
%o A293775 (PARI) Vec((64*x^25 + 448*x^24 + 1184*x^23 + 1784*x^22 + 2028*x^21 + 1948*x^20 + 1080*x^19 + 104*x^18 - 180*x^17 + 540*x^16 + 1156*x^15 + 696*x^14 + 252*x^13 + 238*x^12 + 188*x^11 + 502*x^10 + 806*x^9 + 544*x^8 + 263*x^7 + 185*x^6 + 99*x^5 + 33*x^4 + 13*x^3 + 3*x^2 + x - 1)/(128*x^25 + 896*x^24 + 2368*x^23 + 3568*x^22 + 3928*x^21 + 3064*x^20 + 176*x^19 - 2304*x^18 - 2664*x^17 - 1580*x^16 - 352*x^15 - 576*x^14 - 1104*x^13 - 760*x^12 - 138*x^11 + 686*x^10 + 1238*x^9 + 869*x^8 + 382*x^7 + 210*x^6 + 102*x^5 + 27*x^4 + 12*x^3 + 3*x^2 + 2*x - 1) + O(x^30))
%Y A293775 Cf. A224232, A293774, A293776, A293784.
%K A293775 nonn,easy
%O A293775 0,3
%A A293775 _Bjarki Ágúst Guðmundsson_, Oct 16 2017