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%I #13 Jun 24 2018 13:46:28
%S 0,1,2,8,30,109,401,1495,5623,21289,81034,309817,1188932,4576980,
%T 17667647,68359881,265045494,1029512644,4005417845,15606129991,
%U 60885118375,237816401610,929909358659,3639712494186,14258889345834,55906875628333,219370377887309,861389105627213,3384600499000626
%N G.f.: 2*x*(1-x*sqrt(1-4*x))/((1+2*x^2+sqrt(1-4*x))*sqrt(1-4*x)).
%H G. C. Greubel, <a href="/A278023/b278023.txt">Table of n, a(n) for n = 0..1000</a>
%H J. L. Baril, <a href="http://jl.baril.u-bourgogne.fr/vincular.pdf">Avoiding patterns in irreducible permutations</a>, Discrete Mathematics and Theoretical Computer Science, submitted 2014. See Table 3.
%F a(n) ~ 2^(2*n+2) / (9*sqrt(Pi*n)). - _Vaclav Kotesovec_, Nov 10 2016
%F Conjecture: +n*(3*n^2-12*n+11) *a(n) -(3*n-5) *(3*n^2-9*n+4) *a(n-1) -2*(2*n-5) *(3*n^2-6*n+2) *a(n-2) +n *(3*n^2-12*n+11) *a(n-3) -2 *(2*n-5) *(3*n^2-6*n+2) *a(n-4)=0. - _R. J. Mathar_, Jun 24 2018
%t CoefficientList[Series[2*x*(1-x*Sqrt[1-4*x])/(Sqrt[1-4*x]*(1+2*x^2+Sqrt[1-4*x])), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Nov 10 2016 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(2*x*(1-x*sqrt(1-4*x) )/( (1+ 2*x^2 +sqrt(1-4*x))*sqrt(1-4*x)))) \\ _G. C. Greubel_, Jun 05 2017
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Nov 09 2016