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%I #23 Sep 15 2018 17:56:34
%S 1,1,2,4,7,13,22,38,63,105,169,274,434,686,1069,1660,2548,3897,5906,
%T 8911,13352,19917,29532,43605,64056,93715,136499,198059,286233,412199,
%U 591455,845851,1205687,1713286,2427177,3428611,4829563,6784550,9505840,13284849
%N a(n) is the limiting term of the n-th column of the triangle in A188919.
%H A. M. Baxter, <a href="https://pdfs.semanticscholar.org/2c5d/79e361d3aecb25c380402144177ad7cd9dc8.pdf">Algorithms for Permutation Statistics</a>, Ph. D. Dissertation, Rutgers University, May 2011
%H Andrew M. Baxter and Lara K. Pudwell, <a href="http://arxiv.org/abs/1108.2642">Enumeration schemes for dashed patterns</a>, arXiv preprint arXiv:1108.2642, 2011
%t b[u_, o_] := b[u, o] = Expand[If[u + o == 0, 1, Sum[b[u - j, o + j - 1]*x^(o + j - 1), {j, 1, u}] + Sum[If[u == 0, b[u + j - 1, o - j]*x^(o - j), 0], {j, 1, o}]]];
%t T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][ b[0, n]];
%t Take[T[40], 40] (* _Jean-François Alcover_, Sep 15 2018, after _Alois P. Heinz_ in A188919 *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Apr 13 2011
%E More terms from _Andrew Baxter_, May 17 2011
%E a(30)-a(39) from _Alois P. Heinz_, Nov 14 2015
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