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A386815 Coefficients in q-expansion of E_2^4 * E_4^2, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.

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%I A386815 #5 Aug 03 2025 16:07:45
%S A386815 1,384,19008,-3408384,86384832,390216960,-20773815552,-154767455232,
%T A386815 1360271378880,30429758560128,278226995437440,1749537534970368,
%U A386815 8664534035259648,36062711146189056,131104383085776384,427185615341306880,1270776436150340544,3499300888293305088,9016032242401655616
%N A386815 Coefficients in q-expansion of E_2^4 * E_4^2, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.
%t A386815 terms = 20;
%t A386815 E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
%t A386815 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A386815 CoefficientList[Series[E2[x]^4*E4[x]^2, {x, 0, 20}], x]
%Y A386815 Cf. A006352, A004009, A386787.
%K A386815 sign
%O A386815 0,2
%A A386815 _Vaclav Kotesovec_, Aug 03 2025