This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A126859 #18 Aug 06 2025 17:09:33
%S A126859 0,0,1,20,102,2288,3773,14232,133616,119904,584517,1927900,4013432,
%T A126859 2569296,14394518,8365192,14426496,23381600,151885575,58125708,
%U A126859 269849564,395149888,195967551,828880856,398774464,544543680,4586626939,1018905048,1396485648
%N A126859 Numerators of coefficients in quasimodular form F_3(q) of level 1 and weight 12.
%H A126859 Seiichi Manyama, <a href="/A126859/b126859.txt">Table of n, a(n) for n = 0..1000</a>
%H A126859 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 A126859 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 A126859 F_3(q) = (1/12)*q^2 + (20/3)*q^3 + 102*q^4 + (2288/3)*q^5 + 3773*q^6 + 14232*q^7 + ...
%t A126859 es[2]=1-24*Sum[DivisorSigma[1, n]*q^n, {n, 100}]; es[k_?EvenQ]/; k>2:=1-2*k/BernoulliB[k]*Sum[DivisorSigma[k-1, n]*q^n, {n, 100}]; Numerator[CoefficientList[(15*es[2]^4*es[4] - 6*es[2]^6-12*es[2]^2*es[4]^2 + 7*es[4]^3 + 4*es[2]^3*es[6] - 12*es[2]*es[4]*es[6] + 4*es[6]^2)/35831808, q]][[;; 30]] (* _Shenghui Yang_, Aug 06 2025 *)
%Y A126859 Cf. A126858, A126860, A126861.
%K A126859 nonn,frac
%O A126859 0,4
%A A126859 _N. J. A. Sloane_, Mar 15 2007