A290180 Coefficients in expansion of E_8*Delta^2 where Delta is the generating function of Ramanujan's tau function (A000594).

1, 432, 39960, -1418560, 17312940, -71928864, -462815680, 7500885120, -38038437810, 29000909200, 729783353376, -4661016429888, 13691625085880, -16503845217120, -14982974507520, 45085348093056, 99234456545637, -157805792764560, -1644659689877680

Offset: 2

Author

Seiichi Manyama, Jul 23 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 2..1000
• S. C. Milne, Hankel determinants of Eisenstein series, preprint, arXiv:0009130 [math.NT], 2000.

Crossrefs

E_k*Delta^2: A290178 (k=4), A290048 (k=6), this sequence (k=8), A290181 (k=10), A290182 (k=14).

Cf. A000594, A008410 (E_8).

Programs

Mathematica

terms = 19;
E8[x_] = 1 + 480*Sum[k^7*x^k/(1 - x^k), {k, 1, terms}];
E8[x]*QPochhammer[x]^48 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

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).