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%I #18 Mar 23 2017 04:37:14
%S 1,1,2,6,24,111,531,2519,11726,53547,240448,1064608,4658952,20192022,
%T 86807865,370665585,1573606410,6647552115,27962334180,117185243340,
%U 489508952160,2038937744610,8471179017990,35115582053214,145269385076124,599866065025406,2472955722033776,10179494703130704,41844811399520752,171796056971896588
%N Number of permutations of 1..n that almost avoid 231.
%H G. C. Greubel, <a href="/A174195/b174195.txt">Table of n, a(n) for n = 0..1000</a>
%H R. Brignall et al., <a href="http://dx.doi.org/10.1016/j.disc.2009.06.027">Almost avoiding permutations</a>, Discrete Math., 309 (2009), 6626-6631.
%F G.f.: (1-5*x-6*x^2 + 45*x^3-24*x^4-(1 + x-4*x^2 + x^3)*(1-4*x)^(3/2))/(-2*x^2*(1-4*x)^(3/2)).
%F a(n) ~ 2^(2*n-2)*sqrt(n)/sqrt(Pi). - _Vaclav Kotesovec_, Aug 23 2014
%F Conjecture: 2*(n+2)*(2013*n^2-10435*n+41550)*a(n) +(4026*n^3 -128025*n^2 +34955*n+59010)*a(n-1) -2 *(2*n-5)*(20130*n^2 -110855*n +93819) *a(n-2)=0. - _R. J. Mathar_, Jun 14 2016
%t CoefficientList[Series[(1 - 5*x - 6*x^2 + 45*x^3 - 24*x^4 - (1 + x - 4*x^2 + x^3)*(1 - 4*x)^(3/2))/(-2*x^2*(1 - 4*x)^(3/2)), {x,0,50}], x] (* _G. C. Greubel_, Mar 22 2017 *)
%o (PARI) x='x+O('x^50); Vec((1 - 5*x - 6*x^2 + 45*x^3 - 24*x^4 - (1 + x - 4*x^2 + x^3)*(1 - 4*x)^(3/2))/(-2*x^2*(1 - 4*x)^(3/2))) \\ _G. C. Greubel_, Mar 22 2017
%Y Cf. A174193.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Nov 26 2010
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