A290181 Coefficients in expansion of E_10*Delta^2 where Delta is the generating function of Ramanujan's tau function (A000594).

1, -312, -121680, 1004000, 37942020, -801594864, 6139193600, -11831002560, -151614128250, 1346611783000, -4592794000704, 3738595861728, 15192491492360, 47281379454000, -737660590018560, 2662090686805056, -3290770281735027, -4884703150768920

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), A290180 (k=8), this sequence (k=10), A290182 (k=14).

Cf. A000594, A013974 (E_10).

Programs

Mathematica

terms = 18;
E10[x_] = 1 - 264*Sum[k^9*x^k/(1 - x^k), {k, 1, terms}];
E10[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_10, E_12 ; E_8, E_12, E_14 ; E_10, E_14, E_16]. G.f. is 691^2*3617*b(q)/(1728^2*2^2*3*5^6*7^2*13).