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Coefficients in expansion of E_14*Delta^2 where Delta is the generating function of Ramanujan's tau function (A000594).
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%I #22 Mar 11 2023 06:57:24

%S 1,-72,-194400,-28866400,13994100,9650004336,-99683138560,-1007380800,

%T 5570606272950,-32186306471000,-2717893793664,724443400725408,

%U -2662202398202200,-401005712372400,19385312101171200,24633489938571456,-449375771787124707

%N Coefficients in expansion of E_14*Delta^2 where Delta is the generating function of Ramanujan's tau function (A000594).

%H Seiichi Manyama, <a href="/A290182/b290182.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_8, E_10, E_14 ; E_10, E_12, E_16 ; E_12, E_14, E_18]. G.f. is -691^2*3617*43867*b(q)/(1728^2*2^6*3*5^3*7^2*97*7213).

%t terms = 17;

%t E14[x_] = 1 - 24*Sum[k^13*x^k/(1 - x^k), {k, 1, terms}];

%t E14[x]*QPochhammer[x]^48 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)

%Y E_k*Delta^2: A290178 (k=4), A290048 (k=6), A290180 (k=8), A290181 (k=10), this sequence (k=14).

%Y Cf. A000594, A058550 (E_14).

%K sign

%O 2,2

%A _Seiichi Manyama_, Jul 23 2017