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A321572 Related to the set of Motzkin trees where all leaves are at the same unary height 2. 1

%I

%S 0,1,0,1,1,3,2,9,7,27,25,85,86,287,296,975,1065,3369,3825,11887,13836,

%T 42389,50597,152549,186186,554103,688494,2027304,2559958,7461971,

%U 9561298,27617581,35846863,102707431,134874639,383561963,509090498,1437822479,1927045425

%N Related to the set of Motzkin trees where all leaves are at the same unary height 2.

%C Row 2 of A321396, see section 3.2 in O. Bodini et al.

%H Olivier Bodini, Danièle Gardy, Bernhard Gittenberger, Zbigniew Gołębiewski, <a href="http://arxiv.org/abs/1510.01167">On the number of unary-binary tree-like structures with restrictions on the unary height</a>, arXiv:1510.01167v1 [math.CO], 2015.

%F G.f.: (1 - sqrt(1 - 2*z + 2*z*sqrt(1 - 2*z + 2*z*sqrt(1 - 4*z^2))))/(2*z^3).

%p gf := -(sqrt(2*z*(sqrt(2*z*(sqrt(1-4*z^2)-1)+1)-1)+1)-1)/(2*z^3):

%p series(gf,z,44): seq(coeff(%,z,n), n=0..38);

%t 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 *)

%Y Cf. A321396.

%K nonn

%O 0,6

%A _Peter Luschny_, Nov 14 2018

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Last modified September 25 09:35 EDT 2022. Contains 356977 sequences. (Running on oeis4.)