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 A126861 Coefficients in quasimodular form 12*F_3(q) of level 1 and weight 12. 3

%I

%S 0,0,1,80,1224,9152,45276,170784,534464,1438848,3507102,7711600,

%T 16053728,30831552,57578072,100382304,173117952,280579200,455656725,

%U 697508496,1079398256,1580599552,2351610612,3315523424,4785293568,6534524160,9173253878,12226860576

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

%H Seiichi Manyama, <a href="/A126861/b126861.txt">Table of n, a(n) for n = 0..1000</a>

%H B. Mazur, <a href="https://doi.org/10.1090/S0273-0979-04-01024-9">Perturbations, deformations and variations (and "near-misses") in geometry, physics, and number theory</a>, Bull. Amer. Math. Soc., 41 (2004), 307-336.

%F 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.).

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

%Y Cf. A126858, A126859, A126860.

%Y 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).

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Mar 15 2007

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Last modified August 10 06:23 EDT 2020. Contains 336368 sequences. (Running on oeis4.)