A126860 -id:A126860

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A126859

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

+0
3

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

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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.

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Mar 15 2007

STATUS

approved

A126861

Coefficients in quasimodular form 12*F_3(q) of level 1 and weight 12.

+0
3

0, 0, 1, 80, 1224, 9152, 45276, 170784, 534464, 1438848, 3507102, 7711600, 16053728, 30831552, 57578072, 100382304, 173117952, 280579200, 455656725, 697508496, 1079398256, 1580599552, 2351610612, 3315523424, 4785293568, 6534524160, 9173253878, 12226860576