%I #8 Nov 11 2017 11:51:33

%S 1,1,2,6,21,74,245,744,2068,5296,12608,28150,59412,119341,229477,

%T 424478,758491,1313931,2213350,3635214,5834559,9169668,14136101,

%U 21409620,31899782,46816226,67749956,96772222,136553926,190508831,262964229,359363130,486502469,652812293,868681386,1146835318,1502773465

%N Number of permutations of [n] avoiding {4231, 1423, 1234}.

%H Colin Barker, <a href="/A294765/b294765.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 115.

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

%F G.f.: (1 - 10*x + 46*x^2 - 126*x^3 + 230*x^4 - 289*x^5 + 256*x^6 - 158*x^7 + 66*x^8 - 17*x^9 + 2*x^10) / (1 - x)^11.

%F From _Colin Barker_, Nov 11 2017: (Start)

%F a(n) = (3628800 - 1447200*n + 1660536*n^2 - 377700*n^3 + 154790*n^4 + 9135*n^5 - 987*n^6 + 1350*n^7 + 60*n^8 + 15*n^9 + n^10) / 3628800.

%F a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>10.

%F (End)

%p -(2*x^10-17*x^9+66*x^8-158*x^7+256*x^6-289*x^5+230*x^4-126*x^3+46*x^2-10*x+1)/(x-1)^11 ;

%p taylor(%,x=0,40) ;

%p gfun[seriestolist](%) ;

%o (PARI) Vec((1 - 10*x + 46*x^2 - 126*x^3 + 230*x^4 - 289*x^5 + 256*x^6 - 158*x^7 + 66*x^8 - 17*x^9 + 2*x^10) / (1 - x)^11 + O(x^40)) \\ _Colin Barker_, Nov 11 2017

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 08 2017