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A045722 Number of border edges in all noncrossing rooted trees on n nodes. 2
1, 6, 28, 150, 858, 5096, 31008, 191862, 1201750, 7597590, 48384180, 309939240, 1994981688, 12892738800, 83604224384, 543722433078, 3545056580814, 23164787710610, 151662849838500, 994674967479270, 6533629880128890 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..1208

Index entries for sequences related to rooted trees

FORMULA

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

MATHEMATICA

MapAt[# - 1 &, Array[(# + 1) Binomial[3 # - 2, # - 1]/# &, 21], 1] (* Michael De Vlieger, Mar 19 2021 *)

CROSSREFS

Cf. A026004.

Sequence in context: A163029 A309490 A344755 * A047129 A173081 A278015

Adjacent sequences:  A045719 A045720 A045721 * A045723 A045724 A045725

KEYWORD

nonn

AUTHOR

Emeric Deutsch

STATUS

approved

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Last modified May 22 16:07 EDT 2022. Contains 353957 sequences. (Running on oeis4.)