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%I #12 Nov 08 2017 04:21:13
%S 1,2,6,21,70,195,458,942,1752,3016,4886,7539,11178,16033,22362,30452,
%T 40620,53214,68614,87233,109518,135951,167050,203370,245504,294084,
%U 349782,413311,485426,566925
%N Number of permutations of length n which avoid the patterns 1234, 2431, 4312.
%H D. Callan, T. Mansour, <a href="http://arxiv.org/abs/1705.00933">Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns</a>, arXiv:1705.00933 (2017), Table 2 No 9.
%H Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F G.f.: A(x) = -{(3x^6+6x^5-9x^4+5x^3-9x^2+4x-1)x}/{(x-1)^6}
%F For n >= 2, a(n) = (n^5 + 75n^4 - 715n^3 + 2685n^2 - 4446n + 2880)/120. - Franklin T. Adams-Watters, Sep 16 2006
%p cn := [1,-5,11,-11,10,3,-5,-3] ;
%p p := add(cn[i]*x^(i-1),i=1..nops(cn)) ;
%p q := (1-x)^6 ;
%p taylor(p/q,x=0,40) ;
%p gfun[seriestolist](%) ; # _R. J. Mathar_, Nov 07 2017
%K nonn,easy
%O 1,2
%A _Lara Pudwell_, Feb 26 2006