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 A336009 #5 Jul 05 2020 00:01:02
%S A336009 1,1,1,1,1,2,4,8,16,34,82,226,678,2108,6892,23948,88532,344816,
%T A336009 1401200,5925000,26146360,120743496,582606552,2926675112,15259183112,
%U A336009 82458502624,461577781968,2674216518016,16013654472352,98968416103968,630595248710144
%N A336009 a(0) = ... = a(3) = 1; a(n) = Sum_{k=0..n-4} binomial(n-4,k) * a(k) * a(n-k-4).
%C A336009 Shifts 4 places left when e.g.f. is squared.
%F A336009 E.g.f. A(x) satisfies: A(x) = 1 + x + x^2/2 + x^3/6 + Integral( Integral( Integral( Integral A(x)^2 dx) dx) dx) dx.
%t A336009 a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = Sum[Binomial[n - 4, k] a[k] a[n - k - 4], {k, 0, n - 4}]; Table[a[n], {n, 0, 30}]
%t A336009 nmax = 30; A[_] = 0; Do[A[x_] = 1 + x + x^2/2 + x^3/6 + Integrate[Integrate[Integrate[Integrate[A[x]^2, x], x], x], x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] Range[0, nmax]!
%Y A336009 Cf. A000142, A007558, A307971, A333497, A336010.
%K A336009 nonn
%O A336009 0,6
%A A336009 _Ilya Gutkovskiy_, Jul 04 2020