This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A321572 #17 Feb 12 2021 12:12:32 %S A321572 0,1,0,1,1,3,2,9,7,27,25,85,86,287,296,975,1065,3369,3825,11887,13836, %T A321572 42389,50597,152549,186186,554103,688494,2027304,2559958,7461971, %U A321572 9561298,27617581,35846863,102707431,134874639,383561963,509090498,1437822479,1927045425 %N A321572 Related to the set of Motzkin trees where all leaves are at the same unary height 2. %C A321572 Row 2 of A321396, see section 3.2 in O. Bodini et al. %H A321572 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 A321572 G.f.: (1 - sqrt(1 - 2*z + 2*z*sqrt(1 - 2*z + 2*z*sqrt(1 - 4*z^2))))/(2*z^3). %p A321572 gf := -(sqrt(2*z*(sqrt(2*z*(sqrt(1-4*z^2)-1)+1)-1)+1)-1)/(2*z^3): %p A321572 series(gf,z,44): seq(coeff(%,z,n), n=0..38); %t A321572 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 A321572 Cf. A321396. %K A321572 nonn %O A321572 0,6 %A A321572 _Peter Luschny_, Nov 14 2018