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Coefficients in expansion of E_4*Delta^2 where Delta is the generating function of Ramanujan's tau function (A000594).
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%I #21 Mar 11 2023 06:41:17

%S 1,192,-8280,147200,-1438020,7491456,-4626880,-246965760,2112385950,

%T -9443825600,23625035616,-14413771008,-118710609640,427914230400,

%U -467038103040,-645319017984,1640006523477,2800373100480,-8506579320400,-21655683517440,108181106829972

%N Coefficients in expansion of E_4*Delta^2 where Delta is the generating function of Ramanujan's tau function (A000594).

%H Seiichi Manyama, <a href="/A290178/b290178.txt">Table of n, a(n) for n = 2..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 3 X 3 matrix [E_4, E_8, E_10 ; E_6, E_10, E_12 ; E_8, E_12, E_14]. G.f. is 691^2*b(q)/(1728^2*21^2*250).

%t terms = 21;

%t E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];

%t E4[x]*QPochhammer[x]^48 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)

%Y E_k*Delta^2: this sequence (k=4), A290048 (k=6), A290180 (k=8), A290181 (k=10), A290182 (k=14).

%Y Cf. A000594, A004009 (E_4), A290152.

%K sign

%O 2,2

%A _Seiichi Manyama_, Jul 23 2017