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%I #22 Mar 11 2023 06:39:47
%S 1,168,-12636,392832,-7335174,92207808,-804651624,4626614784,
%T -11834988165,-73870961696,1115908456740,-7498139072256,
%U 32630722986078,-90379426346496,94395618447768,450271639673856,-2625847472007243,6203580643521072,-3151366507609936
%N Coefficients in expansion of E_4*Delta^3 where Delta is the generating function of Ramanujan's tau function (A000594).
%H Seiichi Manyama, <a href="/A290152/b290152.txt">Table of n, a(n) for n = 3..1000</a>
%H S. C. Milne, <a href="https://arxiv.org/abs/math/0009130">Hankel determinants of Eisenstein series</a>, preprint, arXiv:0009130 [math.NT], 2000.
%F Let b(q) be the determinant of the 4 X 4 Hankel matrix [E_4, E_6, E_8, E_10 ; E_6, E_8, E_10, E_12 ; E_8, E_10, E_12, E_14 ; E_10, E_12, E_14, E_16]. G.f. is -691^3*3617*b(q)/(1728^3*2^4*3*5^6*7^2*467).
%t terms = 19;
%t E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t E4[x]*QPochhammer[x]^(3*24) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)
%Y Cf. A000594, A004009 (E_4).
%Y Cf. A290048, A290178.
%K sign
%O 3,2
%A _Seiichi Manyama_, Jul 21 2017
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