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%I #20 Oct 06 2019 09:04:37
%S 1,3,14,81,521,3554,25172,183129,1359863,10264359,78521474,607449380,
%T 4744167924,37355679904,296232263792,2363773540473,18965408058723,
%U 152910824717297,1238260516988018,10066874219853977,82134185988563049,672294915226393926,5519252917557226452
%N Number of Largest Chain Ladder Family (LCLF) matchings on n edges.
%C The Largest Chain Ladder Family (LCLF) of matchings is the largest family of matchings formed by repeated edge inflations by ladders and vertex insertions into a chain of any length.
%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.
%F G.f. f satisfies 2x^3f^6-2x^2f^5+4x^2f^4-3xf^3+2xf^2+f-1=0.
%e a(3)=14 because of the 15 matchings on 3 edges, only one does not lie in the Largest Chain Ladder Family. In canonical sequence form, the missing matching is given by 123123.
%p f := RootOf(2*x^3*_Z^6-2*x^2*_Z^5+4*x^2*_Z^4-3*x*_Z^3+2*x*_Z^2+_Z-1,1);
%p series(f, x=0, 30);
%K nonn
%O 1,2
%A _Aziza Jefferson_, Mar 25 2015