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 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 (list; graph; refs; listen; history; text; internal format)
 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), 195-210; Addendum, 18 (1997), 739-740. FORMULA G.f.: (1/8) * (1 + 1/sqrt(1-4*x)) * (1 + sqrt(1-4*x) - sqrt(2) * sqrt(1 - 10*x + sqrt(1-4*x))), see Klazar's paper. - Sean A. Irvine, Feb 06 2018 a(n) = ((n - 1)/2)*CatalanNumber(n-1)*(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_] := ((n-1)/2) CatalanNumber[n-1](1 - Hypergeometric2F1[-1/2, - n, n-1, -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 EXTENSIONS More terms from Sean A. Irvine, Feb 06 2018 STATUS approved

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Last modified December 14 14:20 EST 2019. Contains 329979 sequences. (Running on oeis4.)