

A007856


Subtrees in rooted plane trees on n nodes.


2



1, 3, 12, 52, 236, 1109, 5366, 26639, 135300, 701269, 3700400, 19834973, 107784622, 592705377, 3292970302, 18458954896, 104276682820, 593056996445, 3392898090908, 19512100041995, 112729617387020, 653965783541960, 3807766434556940
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OFFSET

1,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
G.S. Cheon, H. Kim, L. W. Shapiro, Mutation effects in ordered trees, arXiv preprint arXiv:1410.1249 [math.CO], 2014.
M. Klazar, Twelve countings with rooted plane trees, European Journal of Combinatorics 18 (1997), 195210; Addendum, 18 (1997), 739740.
Index entries for sequences related to rooted trees


FORMULA

G.f.: (1/8) * (1 + 1/sqrt(14*x)) * (1 + sqrt(14*x)  sqrt(2) * sqrt(1  10*x + sqrt(14*x))), see Klazar's paper.  Sean A. Irvine, Feb 06 2018
a(n) = ((n  1)/2)*CatalanNumber(n1)*(1  hypergeom([1/2, n], [n  1], 4)).  Peter Luschny, Aug 04 2019


MATHEMATICA

Rest[CoefficientList[Series[(1/8) (1 + 1/Sqrt[1  4 x]) (1 + Sqrt[1  4 x]  Sqrt[2] Sqrt[1  10 x + Sqrt[1  4 x]]), {x, 0, 33}], x]] (* Vincenzo Librandi, Feb 07 2018 *)
A007856[n_] := ((n1)/2) CatalanNumber[n1](1  Hypergeometric2F1[1/2,  n, n1, 4]); Table[A007856[n], {n, 1, 23}] (* Peter Luschny, Aug 04 2019 *)


CROSSREFS

Sequence in context: A151193 A151194 A268208 * A151195 A151196 A010736
Adjacent sequences: A007853 A007854 A007855 * A007857 A007858 A007859


KEYWORD

nonn


AUTHOR

Martin Klazar


EXTENSIONS

More terms from Sean A. Irvine, Feb 06 2018


STATUS

approved



