A126860 Denominators of coefficients in quasimodular form F_3(q) of level 1 and weight 12.

1, 1, 12, 3, 1, 3, 1, 1, 3, 1, 2, 3, 3, 1, 3, 1, 1, 1, 4, 1, 3, 3, 1, 3, 1, 1, 6, 1, 1, 3, 1, 1, 1, 1, 2, 3, 1, 1, 3, 3, 1, 3, 1, 1, 3, 1, 1, 3, 3, 1, 12, 1, 1, 1, 1, 1, 3, 3, 2, 3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 6, 3, 1, 3, 1, 1, 3, 1, 2, 3, 3, 1, 3, 1, 1, 1, 2, 1, 3, 3, 1, 3, 1, 1, 4, 1, 1

Offset: 0

Author

N. J. A. Sloane, Mar 15 2007

Keywords

• nonn
• frac

Examples

			F_3(q) = (1/12)*q^2 + (20/3)*q^3 + 102*q^4 + (2288/3)*q^5 + 3773*q^6 + 14232*q^7 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• B. Mazur, Perturbations, deformations and variations (and "near-misses") in geometry, physics, and number theory, Bull. Amer. Math. Soc., 41 (2004), 307-336.

Crossrefs

Cf. A126858, A126859, A126861.

Formula

F_3(q) = (15*E(2)^4*E(4) - 6*E(2)^6 - 12*E(2)^2*E(4)^2 + 7*E(4)^3 + 4*E(2)^3*E(6) - 12*E(2)*E(4)*E(6) + 4*E(6)^2)/35831808, where E(k) is the normalized Eisenstein series of weight k (cf. A006352, etc.).

Extensions

More terms from Seiichi Manyama, May 18 2019