This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A045722 #35 Feb 28 2024 08:10:18 %S A045722 1,6,28,150,858,5096,31008,191862,1201750,7597590,48384180,309939240, %T A045722 1994981688,12892738800,83604224384,543722433078,3545056580814, %U A045722 23164787710610,151662849838500,994674967479270,6533629880128890 %N A045722 Number of border edges in all noncrossing rooted trees on n nodes. %H A045722 Michael De Vlieger, <a href="/A045722/b045722.txt">Table of n, a(n) for n = 1..1208</a> %H A045722 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a> %F A045722 a(n) = (n+1)*binomial(3n-2, n-1)/n for n >= 2. [Corrected by _Sean A. Irvine_, Mar 19 2021] %F A045722 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 A045722 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 A045722 a(n) = (n+1) * A006013(n-1) for n >= 2. - _F. Chapoton_, Feb 27 2024 %t A045722 MapAt[# - 1 &, Array[(# + 1) Binomial[3 # - 2, # - 1]/# &, 21], 1] (* _Michael De Vlieger_, Mar 19 2021 *) %Y A045722 Cf. A026004, A006013. %K A045722 nonn %O A045722 1,2 %A A045722 _Emeric Deutsch_