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A386813 Coefficients in q-expansion of E_2^3 * E_4^2, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.

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%I A386813 #5 Aug 03 2025 16:07:53
%S A386813 1,408,28872,-2685984,24039336,776610576,-657274464,-112765274688,
%T A386813 -1315204139160,-9184174537416,-47705529895632,-201727238619744,
%U A386813 -730623451715808,-2340991131399984,-6787572064867008,-18105120840067776,-44991518932447512,-105189400371536208,-233200610257765464
%N A386813 Coefficients in q-expansion of E_2^3 * E_4^2, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.
%t A386813 terms = 20;
%t A386813 E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
%t A386813 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A386813 CoefficientList[Series[E2[x]^3*E4[x]^2, {x, 0, terms}], x]
%Y A386813 Cf. A006352, A004009, A386781, A386785.
%K A386813 sign
%O A386813 0,2
%A A386813 _Vaclav Kotesovec_, Aug 03 2025