A294974
Coefficients in expansion of (E_2^4/E_4)^(1/8).
Original entry on oeis.org
1, -42, 4032, -659904, 118064226, -22406634432, 4407587356032, -888750999070464, 182478248639753472, -37986867560948245674, 7994272624037726124672, -1697243410477799687716416, 362963150140702802158191360, -78095916585903527021840348352
Offset: 0
-
terms = 14;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
(E2[x]^4/E4[x])^(1/8) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
A295815
Coefficients in expansion of E_4^(-1/4).
Original entry on oeis.org
1, -60, 8460, -1459680, 273388620, -53595097560, 10818138134880, -2228446076600640, 465957083177325900, -98553257565313635420, 21034800052217022675960, -4522762142866403196901920, 978397734079422399475947360
Offset: 0
A300147
a(n) = (1/8) * Sum_{d|n} d * A110163(d).
Original entry on oeis.org
-30, 6660, -1536120, 354476040, -81800478900, 18876653594640, -4356063194112240, 1005225129672310800, -231970363216834560390, 53530545369975222475800, -12352954264801690636800360, 2850624405442199478575792160
Offset: 1
A378469
Coefficients in expansion of (1/E_4)^4.
Original entry on oeis.org
1, -960, 567360, -266138880, 108735481920, -40500351480960, 14114830665358080, -4678563821426250240, 1491145606587529742400, -460511820740945555286720, 138585483759128030100927360, -40812342463218781348220286720, 11800049457060387849887324117760, -3358272262154871467174772417214080
Offset: 0
-
nmax = 20; CoefficientList[Series[(1+240*Sum[DivisorSigma[3, k]*x^k, {k, 1, nmax}])^(-4), {x, 0, nmax}], x]
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