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%I #12 Apr 04 2017 03:14:58
%S 1,1,3,13,65,351,1999,11872,73023,462889,3012162,20056509,136274564,
%T 942624033,6624531216,47219125251,340867497305,2488891555146,
%U 18361241675953,136728796412286,1026878910257061,7772561249596928,59253932922240432,454708539839137050
%N Number of indecomposable permutations avoiding the pattern 3214.
%H Vincenzo Librandi, <a href="/A284715/b284715.txt">Table of n, a(n) for n = 1..200</a>
%H A. L. L. Gao, S. Kitaev, P. B. Zhang. <a href="https://arxiv.org/abs/1605.05490">On pattern avoiding indecomposable permutations</a>, arXiv:1605.05490 [math.CO], 2016.
%F a(n) ~ 3^(2*n+7/2) * phi^2 / (16*Pi*n^4), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Apr 02 2017
%t Rest[CoefficientList[Series[1/2*(Sqrt[1-4*x] + 1)*((1 + 5*x - (1-9*x)^(3/4) * (1-x)^(1/4) * HypergeometricPFQ[{-1/4, 3/4}, {1}, 64*x/((x-1)*(1-9*x)^3)])/(6*x^2) - 1), {x, 0, 30}], x]] (* _Vaclav Kotesovec_, Apr 02 2017 *)
%K nonn
%O 1,3
%A _N. J. A. Sloane_, Apr 02 2017
%E More terms from _Vaclav Kotesovec_, Apr 02 2017