%I #13 Nov 10 2017 15:14:14
%S 1,1,2,6,21,71,217,599,1514,3550,7801,16193,31956,60282,109214,190816,
%T 322679,529823,847060,1321888,2017991,3019425,4435575,6406973,9112072,
%U 12775076,17674931,24155587,32637646,43631516,57752196,75735822,98458109,126954829,162444470
%N Number of permutations of [n] avoiding {4231, 3142, 1234}.
%H Colin Barker, <a href="/A294726/b294726.txt">Table of n, a(n) for n = 0..1000</a>
%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 [math.CO] (2017), Table 2 No 28.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F From _Colin Barker_, Nov 10 2017: (Start)
%F G.f.: (1 - 8*x + 29*x^2 - 60*x^3 + 81*x^4 - 70*x^5 + 40*x^6 - 10*x^7 + 2*x^8) / (1 - x)^9.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.
%F a(n) = (40320 - 14640*n + 15724*n^2 - 3780*n^3 + 3885*n^4 - 1680*n^5 + 546*n^6 - 60*n^7 + 5*n^8) / 40320.
%F (End)
%p cn := [1,-8,29,-60,81,-70,40,-10,2] ;
%p p := add(cn[i]*x^(i-1),i=1..nops(cn)) ;
%p q := (1-x)^9 ;
%p taylor(p/q,x=0,40) ;
%p gfun[seriestolist](%) ;
%o (PARI) Vec((1 - 8*x + 29*x^2 - 60*x^3 + 81*x^4 - 70*x^5 + 40*x^6 - 10*x^7 + 2*x^8) / (1 - x)^9 + O(x^40)) \\ _Colin Barker_, Nov 10 2017
%K nonn,easy
%O 0,3
%A _R. J. Mathar_, Nov 07 2017