A037945 Coefficients of unique normalized cusp form Delta_20 of weight 20 for full modular group.

1, 456, 50652, -316352, -2377410, 23097312, -16917544, -383331840, 1403363637, -1084098960, -16212108, -16023861504, 50421615062, -7714400064, -120420571320, -8939761664, 225070099506, 639933818472

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign

Examples

			q^2 + 456*q^4 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• Fernando Q. Gouvêa, Non-ordinary primes: a story, Experimental Mathematics, Volume 6, Issue 3 (1997), 195-205.
• S. C. Milne, Hankel determinants of Eisenstein series, preprint, arXiv:0009130 [math.NT], 2000.
• Index entries for sequences related to modular groups

Crossrefs

Cf. A013967, A290180.

Programs

Mathematica

terms = 18;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms+1}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms+1}];
((E4[x]^3 - E6[x]^2)/12^3)*E4[x]^2 + O[x]^(terms+1) // CoefficientList[#, x]& // Rest (* Jean-François Alcover, Feb 27 2018, after Seiichi Manyama *)

Formula

a(n) == A013967(n) mod 174611. - Seiichi Manyama, Feb 02 2017

G.f.: (E_4(q)^3 - E_6(q)^2)/12^3 * E_4(q)^2. - Seiichi Manyama, Jun 09 2017

G.f.: 691/(1728*441) * (E_8(q)*E_12(q) - E_10(q)^2). - Seiichi Manyama, Jul 25 2017