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 A337556 #15 Oct 13 2020 23:51:12
%S A337556 1,1,7,57,607,8121,130527,2447257,52435327,1263925881,33851510047,
%T A337556 997303255257,32052722909247,1116001351341241,41845542004844767,
%U A337556 1681112968022124057,72039936723424794367,3280036569708658302201,158127582939120607830687,8046697501049910668173657
%N A337556 a(0) = 1; a(n) = (1/3) * Sum_{k=1..n} binomial(n,k) * (4^k-1) * a(n-k).
%H A337556 Robert Israel, <a href="/A337556/b337556.txt">Table of n, a(n) for n = 0..387</a>
%F A337556 E.g.f.: 3 / (3 + exp(x) - exp(4*x)).
%F A337556 a(n) ~ n! * (r^3 - 1) * (4*r^3 - 16*r^2 + 64*r - 3) / (771 * log(r)^(n+1)), where r = 1.452626878833844... is the positive real root of the equation r*(r^3 - 1) = 3. - _Vaclav Kotesovec_, Aug 31 2020
%p A337556 E:= 3 / (3 + exp(x) - exp(4*x)):
%p A337556 S:= series(E,x,41):
%p A337556 seq(n!*coeff(S,x,n),n=0..40); # _Robert Israel_, Oct 13 2020
%t A337556 a[0] = 1; a[n_] := a[n] = (1/3) Sum[Binomial[n, k] (4^k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
%t A337556 nmax = 19; CoefficientList[Series[3/(3 + Exp[x] - Exp[4 x]), {x, 0, nmax}], x] Range[0, nmax]!
%o A337556 (PARI) seq(n)={Vec(serlaplace(3 / (3 + exp(x + O(x*x^n)) - exp(4*x + O(x*x^n)))))} \\ _Andrew Howroyd_, Aug 31 2020
%Y A337556 Cf. A000556, A002450, A337555.
%K A337556 nonn
%O A337556 0,3
%A A337556 _Ilya Gutkovskiy_, Aug 31 2020