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%I #19 May 08 2022 22:58:00
%S 1,1,2,6,24,120,720,5038,40004,347348,3165888,29362568,272387290,
%T 2509750674,22933267716,207994616888,1875239211676,16832320088082,
%U 150613964836684,1344743911906806,11988640129482008,106774648037691852,950340529566921394,8454752823292244122
%N The number of permutations of length n that can be sorted by 5 pop stacks in parallel.
%H R. Smith and V. Vatter, <a href="https://www.semanticscholar.org/paper/The-enumeration-of-permutations-sortable-by-pop-in-Smith-Vatter/653c589cffdddc1f6964e1741574742cc7b00546">The enumeration of permutations sortable by pop stacks in parallel</a>
%F G.f.: (-1 -244911168*x^14 +51*x +424049816*x^13 +16848*x^3 -1189*x^2 -162623*x^4 +1135115*x^5 -5933360*x^6 +93180816*x^15 +176551085*x^9 +475936304*x^11 +23718538*x^7 -330046233*x^10 +1620000*x^17 -73376545*x^8 -20032128*x^16 -521745326*x^12)/(9720000*x^17 -68563152*x^16 +235662840*x^15 -511522200*x^14 +774005724*x^13 -859429792*x^12 +721925168*x^11 -467470314*x^10 +235918701*x^9 -93247962*x^8 +28849981*x^7 -6944099*x^6 +1283865*x^5 -178422*x^4 +17989*x^3 -1239*x^2 +52*x -1).
%K nonn,easy
%O 0,3
%A _Vincent Vatter_, Aug 29 2009