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 A354734 #7 Jun 06 2022 02:52:14
%S A354734 1,1,3,6,21,54,189,558,1944,6210,21681,72576,254988,878850,3112101,
%T A354734 10935000,39030660,139001346,499808232,1797731496,6506661798,
%U A354734 23583173328,85847830965,313063862436,1145325387114,4197826175634,15424343762184,56774049331356,209400739623054
%N A354734 a(0) = a(1) = 1; a(n) = 3 * Sum_{k=0..n-2} a(k) * a(n-k-2).
%F A354734 G.f. A(x) satisfies: A(x) = 1 + x + 3 * (x * A(x))^2.
%F A354734 G.f.: (1 - sqrt(1 - 12 * x^2 * (1 + x))) / (6 * x^2).
%F A354734 a(n) ~ sqrt((2+3*r)*(1+r)) / (sqrt(Pi) * n^(3/2) * r^n), where r = 2*cos(arccos(1/8)/3)/3 - 1/3. - _Vaclav Kotesovec_, Jun 04 2022
%t A354734 a[0] = a[1] = 1; a[n_] := a[n] = 3 Sum[a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 28}]
%t A354734 nmax = 28; CoefficientList[Series[(1 - Sqrt[1 - 12 x^2 (1 + x)])/(6 x^2), {x, 0, nmax}], x]
%Y A354734 Cf. A005159, A007477, A354733, A354735, A354736.
%K A354734 nonn
%O A354734 0,3
%A A354734 _Ilya Gutkovskiy_, Jun 04 2022