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 A289638 #25 Jul 11 2017 08:46:39
%S A289638 -480,106560,-24577920,5671616640,-1308807662400,302026457514240,
%T A289638 -69697011105795840,16083602074756972800,-3711525811469352966240,
%U A289638 856488725919603559612800,-197647268236827050188805760,45609990487075191657212674560
%N A289638 Coefficients in expansion of -q*E'_8/E_8 where E_8 is the Eisenstein Series (A008410).
%H A289638 Seiichi Manyama, <a href="/A289638/b289638.txt">Table of n, a(n) for n = 1..422</a>
%F A289638 a(n) = Sum_{d|n} d * A288471(d).
%F A289638 a(n) = 2*A288261(n)/3 + 16*A000203(n).
%F A289638 a(n) = -Sum_{k=1..n-1} A008410(k)*a(n-k) - A008410(n)*n.
%F A289638 G.f.: 2/3 * E_6/E_4 - 2/3 * E_2 = 2/3 * E_10/E_8 - 2/3 * E_2.
%F A289638 a(n) ~ 2 * (-1)^n * exp(Pi*sqrt(3)*n). - _Vaclav Kotesovec_, Jul 09 2017
%t A289638 nmax = 20; Rest[CoefficientList[Series[-480*x*Sum[k*DivisorSigma[7, k]*x^(k-1), {k, 1, nmax}]/(1 + 480*Sum[DivisorSigma[7, k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Jul 09 2017 *)
%Y A289638 -q*E'_k/E_k: A289635 (k=2), A289636 (k=4), A289637 (k=6), this sequence (k=8), A289639 (k=10), A289640 (k=14).
%Y A289638 Cf. A006352 (E_2), A008410 (E_8), A287933, A288471.
%K A289638 sign
%O A289638 1,1
%A A289638 _Seiichi Manyama_, Jul 09 2017