A290152 Coefficients in expansion of E_4*Delta^3 where Delta is the generating function of Ramanujan's tau function (A000594).

1, 168, -12636, 392832, -7335174, 92207808, -804651624, 4626614784, -11834988165, -73870961696, 1115908456740, -7498139072256, 32630722986078, -90379426346496, 94395618447768, 450271639673856, -2625847472007243, 6203580643521072, -3151366507609936

Offset: 3

Author

Seiichi Manyama, Jul 21 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 3..1000
• S. C. Milne, Hankel determinants of Eisenstein series, preprint, arXiv:0009130 [math.NT], 2000.

Crossrefs

Cf. A000594, A004009 (E_4).

Cf. A290048, A290178.

Programs

Mathematica

terms = 19;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E4[x]*QPochhammer[x]^(3*24) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

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).