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A126860 Denominators of coefficients in quasimodular form F_3(q) of level 1 and weight 12. 3

%I

%S 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,

%T 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,

%U 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

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

%H Seiichi Manyama, <a href="/A126860/b126860.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 F_3(q) = (1/12)*q^2 + (20/3)*q^3 + 102*q^4 + (2288/3)*q^5 + 3773*q^6 + 14232*q^7 + ...

%Y Cf. A126858, A126859, A126861.

%K nonn,frac

%O 0,3

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

%E More terms from _Seiichi Manyama_, May 18 2019

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Last modified August 9 18:32 EDT 2020. Contains 336326 sequences. (Running on oeis4.)