|
%I #22 Mar 11 2023 06:42:16
%S 1,432,39960,-1418560,17312940,-71928864,-462815680,7500885120,
%T -38038437810,29000909200,729783353376,-4661016429888,13691625085880,
%U -16503845217120,-14982974507520,45085348093056,99234456545637,-157805792764560,-1644659689877680
%N Coefficients in expansion of E_8*Delta^2 where Delta is the generating function of Ramanujan's tau function (A000594).
%H Seiichi Manyama, <a href="/A290180/b290180.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_6, E_8, E_12 ; E_8, E_10, E_14 ; E_10, E_12, E_16]. G.f. is -691^2*3617*b(q)/(1728^2*2^3*3*5^3*7^2*467).
%t terms = 19;
%t E8[x_] = 1 + 480*Sum[k^7*x^k/(1 - x^k), {k, 1, terms}];
%t E8[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), this sequence (k=8), A290181 (k=10), A290182 (k=14).
%Y Cf. A000594, A008410 (E_8).
%K sign
%O 2,2
%A _Seiichi Manyama_, Jul 23 2017
|
