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A321572
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Related to the set of Motzkin trees where all leaves are at the same unary height 2.
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1
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0, 1, 0, 1, 1, 3, 2, 9, 7, 27, 25, 85, 86, 287, 296, 975, 1065, 3369, 3825, 11887, 13836, 42389, 50597, 152549, 186186, 554103, 688494, 2027304, 2559958, 7461971, 9561298, 27617581, 35846863, 102707431, 134874639, 383561963, 509090498, 1437822479, 1927045425
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OFFSET
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0,6
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COMMENTS
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Row 2 of A321396, see section 3.2 in O. Bodini et al.
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LINKS
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Table of n, a(n) for n=0..38.
Olivier Bodini, Danièle Gardy, Bernhard Gittenberger, Zbigniew Gołębiewski, On the number of unary-binary tree-like structures with restrictions on the unary height, arXiv:1510.01167v1 [math.CO], 2015.
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FORMULA
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G.f.: (1 - sqrt(1 - 2*z + 2*z*sqrt(1 - 2*z + 2*z*sqrt(1 - 4*z^2))))/(2*z^3).
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MAPLE
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gf := -(sqrt(2*z*(sqrt(2*z*(sqrt(1-4*z^2)-1)+1)-1)+1)-1)/(2*z^3):
series(gf, z, 44): seq(coeff(%, z, n), n=0..38);
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MATHEMATICA
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CoefficientList[(1 - Sqrt[2 Sqrt[2 Sqrt[1 - 4z^2] z - 2z + 1] z - 2z + 1])/ (2z^3) + O[z]^40, z] (* Jean-François Alcover, Jun 03 2019 *)
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CROSSREFS
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Cf. A321396.
Sequence in context: A237651 A124003 A159588 * A118045 A276023 A268822
Adjacent sequences: A321569 A321570 A321571 * A321573 A321574 A321575
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KEYWORD
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nonn
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AUTHOR
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Peter Luschny, Nov 14 2018
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STATUS
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approved
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