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%I #26 Aug 25 2013 14:23:32
%S 1,4,14,47,157,529,1805,6238,21812,77062,274738,987276,3572568,
%T 13007398,47617798,175171543,647227453,2400843823,8937670603,
%U 33380986153,125045165773,469700405533,1768752809221,6676088636479,25252913322299,95712549267151,363441602176007,1382467779393307,5267219868722803
%N The number of boundary edges for all ordered trees with n edges.
%C Apparently partial sums of A071722. - _R. J. Mathar_, Aug 25 2013
%F G.f.: (x*C+2*x^2*C^4)/(1-x) where C is the g.f. for the Catalan numbers A000108.
%F Conjecture: 2*(n+3)*a(n) +2*(-7*n-11)*a(n-1) +(29*n+7)*a(n-2) +(-21*n+19)*a(n-3) +2*(2*n-5)*a(n-4)=0. - _R. J. Mathar_, Aug 25 2013
%e The 5 ordered trees with 3 edges have 3,3,2,3,3 boundary edges with UDUDUD having but 2.
%o (PARI)
%o x = 'x + O('x^66);
%o C = serreverse( x/( 1/(1-x) ) ) / x; \\ Catalan A000108
%o gf = (x*C+2*x^2*C^4)/(1-x);
%o Vec(gf) \\ _Joerg Arndt_, Aug 21 2013
%Y Cf. A000108.
%K nonn
%O 0,2
%A _Louis Shapiro_, Aug 20 2013
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