A288990
Define the exponents b(1), b(2), ... such that E_12 is equal to (1-q)^b(1) (1-q^2)^b(2) (1-q^3)^b(3) ... . a(n) = b(n) * A288989(n).
Original entry on oeis.org
-65520, -90598009320, 442356959924880, 4181653887366701917080, -42458488603945952980072176, -254774947034575235293755006524520, 3880639008647135220484579615019041680, 17460929863645555627595091312548802016985880
Offset: 1
b(1) = 24 + 1/1 * A008683(1/1) * A288472(1)/A288989(1) = 24 + 1/1 * (-82104/691) = -65520/691,
b(2) = 24 + 1/2 * (A008683(2/1) * A288472(1)/A288989(1) + A008683(2/2) * A288472(2)/A288989(2)) = 24 + 1/2 * (82104/691 - 181275671592/477481) = -90598009320/477481.
A289247
Coefficients in expansion of 1/E_4^(1/8).
Original entry on oeis.org
1, -30, 3780, -616440, 111056910, -21135698280, 4165203862440, -840914061328320, 172810940671692900, -35998781800053352710, 7579904611028433074280, -1609957152292592382408360, 344417407415742189796786680, -74127324674775434904036905640
Offset: 0
E_4^(k/8):
A001943 (k=-8),
A289566 (k=-4),
A295815 (k=-2), this sequence (k=-1),
A108091 (k=1),
A289307 (k=2),
A289308 (k=3),
A289292 (k=4),
A289309 (k=5),
A289318 (k=6),
A289319 (k=7),
A004009 (k=8).
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nmax = 20; CoefficientList[Series[(1 + 240*Sum[DivisorSigma[3,k]*x^k, {k, 1, nmax}])^(-1/8), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 09 2017 *)