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%I #35 Feb 28 2024 08:10:18
%S 1,6,28,150,858,5096,31008,191862,1201750,7597590,48384180,309939240,
%T 1994981688,12892738800,83604224384,543722433078,3545056580814,
%U 23164787710610,151662849838500,994674967479270,6533629880128890
%N Number of border edges in all noncrossing rooted trees on n nodes.
%H Michael De Vlieger, <a href="/A045722/b045722.txt">Table of n, a(n) for n = 1..1208</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F a(n) = (n+1)*binomial(3n-2, n-1)/n for n >= 2. [Corrected by _Sean A. Irvine_, Mar 19 2021]
%F G.f.: (1+g-7*g^2+3*g^3)/((1-3*g)*(g-1)^2) where g*(1-g)^2 = x. - _Mark van Hoeij_, Nov 10 2011
%F D-finite with recurrence 2*n*(2*n-1)*a(n) + (-43*n^2+83*n-34)*a(n-1) + 12*(3*n-5)*(3*n-7)*a(n-2) = 0. - _R. J. Mathar_, Jul 26 2022
%F a(n) = (n+1) * A006013(n-1) for n >= 2. - _F. Chapoton_, Feb 27 2024
%t MapAt[# - 1 &, Array[(# + 1) Binomial[3 # - 2, # - 1]/# &, 21], 1] (* _Michael De Vlieger_, Mar 19 2021 *)
%Y Cf. A026004, A006013.
%K nonn
%O 1,2
%A _Emeric Deutsch_
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