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 A307733 #35 Jul 05 2020 23:36:25
%S A307733 1,1,4,14,54,220,934,4090,18344,83850,389214,1829736,8693962,41685714,
%T A307733 201442188,980091814,4797070022,23603701828,116688837886,579312087802,
%U A307733 2887020896016,14437318756818,72424982972862,364366674463824,1837954750285458
%N A307733 a(0) = a(1) = 1; a(n) = a(n-1) + a(n-2) + Sum_{k=0..n-1} a(k) * a(n-k-1).
%F A307733 G.f. A(x) satisfies: A(x) = (1 - x + x*A(x)^2) / (1 - x - x^2).
%F A307733 G.f.: (1 - x - x^2 - sqrt(1 - 6*x + 3*x^2 + 2*x^3 + x^4)) / (2*x).
%t A307733 a[0] = a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + Sum[a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 24}]
%t A307733 nmax = 24; CoefficientList[Series[(1 - x - x^2 - Sqrt[1 - 6 x + 3 x^2 + 2 x^3 + x^4])/(2 x), {x, 0, nmax}], x]
%Y A307733 Cf. A002212, A004148, A006318, A085139, A128720, A143330, A171416, A175934, A245734.
%K A307733 nonn
%O A307733 0,3
%A A307733 _Ilya Gutkovskiy_, Jul 05 2020