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A126861 Coefficients in quasimodular form 12*F_3(q) of level 1 and weight 12. 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 (list; graph; refs; listen; history; text; internal format)
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

12*F_3(q) = q^2 + 80*q^3 + 1224*q^4 + 9152*q^5 + 45276*q^6 + 170784*q^7 + 534464*q^8 + ...

CROSSREFS

Cf. A126858, A126859, A126860.

Cf. A280024 (E_2^4*E_4), A308285 (E_2^6), A282752 (E_2^2*E_4^2), A008411 (E_4^3), A282780 (E_2^3*E_6), A282102 (E_2*E_4*E_6), A280869 (E_6^2).

Sequence in context: A275701 A168364 A296353 * A038727 A204476 A151603

Adjacent sequences:  A126858 A126859 A126860 * A126862 A126863 A126864

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 15 2007

STATUS

approved

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Last modified July 15 23:32 EDT 2020. Contains 335774 sequences. (Running on oeis4.)