%I #20 Mar 01 2018 02:37:08
%S 1,264,8568,231456,6214872,166719024,4472485344,119980322880,
%T 3218631807384,86344077536616,2316294684846288,62137684699355232,
%U 1666926011246777184,44717506621139113584,1199606572169515887552,32181041313068138778816
%N Coefficients in expansion of E_4/E_2.
%H Seiichi Manyama, <a href="/A288877/b288877.txt">Table of n, a(n) for n = 0..699</a>
%F a(n) ~ 12 / r^n, where r = A211342 = 0.037276810296451658150980785651644618... is the root of the equation Sum_{k>=1} A000203(k) * r^k = 1/24. - _Vaclav Kotesovec_, Jun 28 2017
%t nmax = 20; CoefficientList[Series[(1 + 240*Sum[DivisorSigma[3, k]*x^k, {k, 1, nmax}])/(1 - 24*Sum[DivisorSigma[1, k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 28 2017 *)
%t terms = 16; Ei[n_] = 1-(2n/BernoulliB[n]) Sum[k^(n-1) x^k/(1-x^k), {k, terms}]; CoefficientList[Ei[4]/Ei[2] + O[x]^terms, x] (* _Jean-François Alcover_, Mar 01 2018 *)
%Y E_{k+2}/E_k: this sequence (k=2), A288261 (k=4), A288840 (k=6).
%Y Cf. A004009 (E_4), A006352 (E_2), A288816 (1/E_2).
%Y Cf. A211342.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jun 18 2017