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%I #18 Oct 06 2019 09:04:29
%S 1,3,15,93,639,4670,35607,280069,2255979,18516875,154313881,
%T 1302252294,11106135906,95571461319,828803505465,7235996887013,
%U 63549647848195,561049960940540,4976419846070007,44325237810194705,396301576614077927,3555397444230816343,31996727212476905751,288776859922595203094,2613107152879937592054,23702850369539462227046,215483061767106353850246,1963017891713523908516093,17917224620763719834090179,163830901587493323034301583,1500542646711279198177939831,13765184019931774406496702885
%N Number of Largest Chain Family matchings on n edges.
%C The Largest Chain Family of matchings is the largest family of matchings formed by repeated edge inflations and vertex insertions into any length n chain.
%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 x^3f^6+x^2f^5-4x^2f^4+2xf^3+(x+4)f^2-11f+7 = 0.
%e a(4)=93 because of the 105 matchings on 4 edges, there are 13 matchings which do not lie in the Largest Chain Family. Two such matching in canonical sequence form, are given by 12343142 and 12342413.
%p f := RootOf(_Z^6*x^3+_Z^5*x^2-4*_Z^4*x^2+2*_Z^3*x+_Z^2*x+4*_Z^2-11*_Z+7, 1);
%p series(f, x=0, 30);
%K nonn
%O 1,2
%A _Aziza Jefferson_, Mar 25 2015
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