A288877 Coefficients in expansion of E_4/E_2.

1, 264, 8568, 231456, 6214872, 166719024, 4472485344, 119980322880, 3218631807384, 86344077536616, 2316294684846288, 62137684699355232, 1666926011246777184, 44717506621139113584, 1199606572169515887552, 32181041313068138778816

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..699

Formula

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

Mathematica

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 *)
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 *)

Crossrefs

E_{k+2}/E_k: this sequence (k=2), A288261 (k=4), A288840 (k=6).

Cf. A004009 (E_4), A006352 (E_2), A288816 (1/E_2).

Cf. A211342.

Sequence in context: A223339 A022043 A035315 * A278409 A168196 A264682

Adjacent sequences: A288874 A288875 A288876 * A288878 A288879 A288880

Keyword

nonn

Author

Seiichi Manyama, Jun 18 2017

Status

approved