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A045722
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Number of border edges in all noncrossing rooted trees on n nodes.
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2
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1, 6, 28, 150, 858, 5096, 31008, 191862, 1201750, 7597590, 48384180, 309939240, 1994981688, 12892738800, 83604224384, 543722433078, 3545056580814, 23164787710610, 151662849838500, 994674967479270, 6533629880128890
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (n+1)*binomial(3n-2, n-1)/n for n >= 2. [Corrected by Sean A. Irvine, Mar 19 2021]
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
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
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MATHEMATICA
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MapAt[# - 1 &, Array[(# + 1) Binomial[3 # - 2, # - 1]/# &, 21], 1] (* Michael De Vlieger, Mar 19 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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