A290178 Coefficients in expansion of E_4*Delta^2 where Delta is the generating function of Ramanujan's tau function (A000594).

1, 192, -8280, 147200, -1438020, 7491456, -4626880, -246965760, 2112385950, -9443825600, 23625035616, -14413771008, -118710609640, 427914230400, -467038103040, -645319017984, 1640006523477, 2800373100480, -8506579320400, -21655683517440, 108181106829972

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: this sequence (k=4), A290048 (k=6), A290180 (k=8), A290181 (k=10), A290182 (k=14).

Cf. A000594, A004009 (E_4), A290152.

Programs

Mathematica

terms = 21;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E4[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_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).