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A007856
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Subtrees in rooted plane trees on n nodes.
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2
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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
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1,2
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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