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 A367982 #10 Jun 11 2024 19:11:36
%S A367982 1,2,36,584,13584,391712,13563456,547900544,25294512384,1313721631232,
%T A367982 75811987301376,4812437436975104,333258221996150784,
%U A367982 25001079178900938752,2019860245103282896896,174842541533954981003264,16143645926877401603702784,1583744338598987290588086272
%N A367982 Expansion of e.g.f. exp(-2*x) / (2 - exp(4*x)).
%H A367982 G. C. Greubel, <a href="/A367982/b367982.txt">Table of n, a(n) for n = 0..345</a>
%F A367982 a(n) = Sum_{k>=0} (4*k-2)^n / 2^(k+1).
%F A367982 a(n) = (-2)^n + Sum_{k=1..n} binomial(n,k) * 4^k * a(n-k).
%F A367982 a(n) = Sum_{k=0..n} binomial(n,k) * (-2)^(n+k) * A000670(k).
%t A367982 nmax = 17; CoefficientList[Series[Exp[-2 x]/(2 - Exp[4 x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A367982 a[n_] := a[n] = (-2)^n + Sum[Binomial[n, k] 4^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 17}]
%o A367982 (Magma)
%o A367982 R<x>:=PowerSeriesRing(Rationals(), 40);
%o A367982 Coefficients(R!(Laplace( Exp(-2*x)/(2-Exp(4*x)) ))); // _G. C. Greubel_, Jun 11 2024
%o A367982 (SageMath)
%o A367982 def A367982_list(prec):
%o A367982 P.<x> = PowerSeriesRing(QQ, prec)
%o A367982 return P( exp(-2*x)/(2-exp(4*x)) ).egf_to_ogf().list()
%o A367982 A367982_list(40) # _G. C. Greubel_, Jun 11 2024
%Y A367982 Cf. A000670, A328183, A344037, A355219, A367977, A367979, A367980, A367981, A367983.
%K A367982 nonn
%O A367982 0,2
%A A367982 _Ilya Gutkovskiy_, Dec 07 2023