A126859 Numerators of coefficients in quasimodular form F_3(q) of level 1 and weight 12.

0, 0, 1, 20, 102, 2288, 3773, 14232, 133616, 119904, 584517, 1927900, 4013432, 2569296, 14394518, 8365192, 14426496, 23381600, 151885575, 58125708, 269849564, 395149888, 195967551, 828880856, 398774464, 544543680, 4586626939, 1018905048, 1396485648

Offset

0,4

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.

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.).

Example

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

Crossrefs

Cf. A126858, A126860, A126861.

Sequence in context: A297585 A113599 A077757 * A071334 A241355 A220207

Adjacent sequences: A126856 A126857 A126858 * A126860 A126861 A126862

Keyword

nonn,frac

Author

N. J. A. Sloane, Mar 15 2007

Status

approved