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%I #4 Aug 03 2025 16:07:42
%S 1,672,145152,8663424,-337036224,-6505531200,40579467264,
%T 1996981485312,25931378854080,210242562994464,1273050737441280,
%U 6245511315490944,26057670474216192,95466371280176064,314217417062264832,945050326572360960,2631525623493208512,6854684254893824832
%N Coefficients in q-expansion of E_2^2 * E_4^3, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.
%t terms = 20;
%t E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
%t E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t CoefficientList[Series[E2[x]^2*E4[x]^3, {x, 0, 20}], x]
%Y Cf. A006352, A004009, A386787.
%K sign
%O 0,2
%A _Vaclav Kotesovec_, Aug 03 2025