%I #27 Oct 06 2019 09:03:56
%S 1,3,14,84,592,4659,39699,359004
%N Number of H&S Family matchings on n edges.
%C The H&S Family of matchings is the family of matchings that can be drawn in the plane without crossings.
%C Jay Pantone has computed the first 1500 terms and has a conjectured g.f. - _N. J. A. Sloane_, Oct 06 2016
%H Michael Albert and Mireille Bousquet-Mélou. <a href="http://arxiv.org/abs/1312.4487">Permutations sortable by two stacks in parallel and quarter plane walks</a>, European Journal of Combinatorics 43 (2015): 131-164. Also arXiv:1312.4487 [math.CO], 2013-2014.
%H C. Haslinger and P. F. Stadler, <a href="http://dx.doi.org/10.1006/bulm.1998.0085">RNA structures with pseudo-notes: Graph-theoretical, combinatorial, and statistical properties</a>, Bulletin of Mathematical Biology 61 (1999), 437-467.
%H Aziza Jefferson, <a href="http://ufdc.ufl.edu/UFE0047620">The Substitution Decomposition of Matchings and RNA Secondary Structures</a>, PhD Thesis, University of Florida, 2015.
%H Jay Pantone, <a href="https://vimeo.com/185888450">Approximate Asymptotic Analysis of Combinatorial Sequences</a>, Experimental Math Seminar, Rutgers University, Oct 06 2016.
%e a(5)= 592; in canonical sequence form the two 3-noncrossing matchings it does not include are 1231435425 and 1234254153.
%K nonn,more
%O 1,2
%A _Aziza Jefferson_, Mar 25 2015