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A126859 Numerators of coefficients in quasimodular form F_3(q) of level 1 and weight 12. 3

%I

%S 0,0,1,20,102,2288,3773,14232,133616,119904,584517,1927900,4013432,

%T 2569296,14394518,8365192,14426496,23381600,151885575,58125708,

%U 269849564,395149888,195967551,828880856,398774464,544543680,4586626939,1018905048,1396485648

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

%H Seiichi Manyama, <a href="/A126859/b126859.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, A126860, A126861.

%K nonn,frac

%O 0,4

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

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Last modified August 9 05:12 EDT 2020. Contains 336319 sequences. (Running on oeis4.)