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A386817 Coefficients in q-expansion of E_2^3 * E_4 * E_6, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.

%I A386817 #4 Aug 03 2025 16:07:39
%S A386817 1,-336,-114912,4151616,100931712,-2848456800,-37865826432,
%T A386817 222362076288,7928555745600,86986313152368,620751040620480,
%U A386817 3392046804500928,15293330001535488,59435665658243616,204976008706800384,640351567531186560,1840291945275505344,4923361835292283488
%N A386817 Coefficients in q-expansion of E_2^3 * E_4 * E_6, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
%t A386817 terms = 20;
%t A386817 E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
%t A386817 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A386817 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t A386817 CoefficientList[Series[E2[x]^3*E4[x]*E6[x], {x, 0, 20}], x]
%Y A386817 Cf. A006352, A004009, A013973, A386787.
%K A386817 sign
%O A386817 0,2
%A A386817 _Vaclav Kotesovec_, Aug 03 2025