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 A059279 #24 Mar 03 2024 14:43:22
%S A059279 1,2,6,20,72,276,1112,4656,20080,88608,398144,1815248,8375904,
%T A059279 39037120,183493440,868853120,4140414720,19841656960,95559048960,
%U A059279 462268075520,2245165391360,10943794652160,53519094753280,262510076263680,1291131867203072
%N A059279 G.f. is ((1-x)/(1-2*x)) * G(x*(1-x)/(1-2*x)) where G(x) is g.f. for Catalan numbers A000108.
%C A059279 Hankel transform is A134751. Binomial transform of A105864. [From _Paul Barry_, Oct 07 2008]
%H A059279 G. C. Greubel, <a href="/A059279/b059279.txt">Table of n, a(n) for n = 0..1000</a>
%H A059279 Ricardo Gómez Aíza, <a href="https://arxiv.org/abs/2402.16111">Trees with flowers: A catalog of integer partition and integer composition trees with their asymptotic analysis</a>, arXiv:2402.16111 [math.CO], 2024. See p. 18.
%F A059279 Conjecture: (n+1)*a(n) +2*(1-4*n)*a(n-1) + 4*(4*n-5)*a(n-2) +4*(5-2*n)*a(n-3)=0. - _R. J. Mathar_, Nov 15 2011
%F A059279 G.f.: (1 - sqrt(1 - 4*x*(1 - x)/(1 - 2*x)))/(2*x). - _G. C. Greubel_, Jan 04 2017
%F A059279 G.f. A(x) satisfies: A(x) = 1 + x * (1/(1 - 2*x) + A(x)^2). - _Ilya Gutkovskiy_, Jun 30 2020
%F A059279 a(n) ~ 5^(1/4) * 2^(n-1) * phi^(2*n + 3/2) / (sqrt(Pi) * n^(3/2)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Jun 30 2020
%t A059279 CoefficientList[Series[(1 - Sqrt[1 - 4*t*(1 - t)/(1 - 2*t)])/(2*t), {t, 0, 50}], t] (* _G. C. Greubel_, Jan 04 2017 *)
%o A059279 (PARI) Vec((1 - sqrt(1 - 4*t*(1 - t)/(1 - 2*t)))/(2*t) + O(t^50)) \\ _G. C. Greubel_, Jan 04 2017
%K A059279 nonn
%O A059279 0,2
%A A059279 _N. J. A. Sloane_, Jan 24 2001