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 A337555 #11 Sep 01 2020 03:35:16
%S A337555 1,1,6,43,408,4861,69516,1159663,22108848,474192601,11300589876,
%T A337555 296237533483,8471642214888,262456441714741,8756520140416236,
%U A337555 313017838828154503,11935355244756882528,483537933291091103281,20741938090482567562596,939180816648348685174723
%N A337555 a(0) = 1; a(n) = (1/2) * Sum_{k=1..n} binomial(n,k) * (3^k-1) * a(n-k).
%F A337555 E.g.f.: 2 / (2 + exp(x) - exp(3*x)).
%F A337555 a(n) ~ n! / ((r+3) * log(r)^(n+1)), where r = 1.52137970680456756960408... is the real root of the equation r^3 - r = 2. - _Vaclav Kotesovec_, Aug 31 2020
%t A337555 a[0] = 1; a[n_] := a[n] = (1/2) Sum[Binomial[n, k] (3^k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
%t A337555 nmax = 19; CoefficientList[Series[2/(2 + Exp[x] - Exp[3 x]), {x, 0, nmax}], x] Range[0, nmax]!
%o A337555 (PARI) seq(n)={Vec(serlaplace(2 / (2 + exp(x + O(x*x^n)) - exp(3*x + O(x*x^n)))))} \\ _Andrew Howroyd_, Aug 31 2020
%Y A337555 Cf. A000556, A003462, A337556.
%K A337555 nonn
%O A337555 0,3
%A A337555 _Ilya Gutkovskiy_, Aug 31 2020