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A386814 Coefficients in q-expansion of E_2^4 * E_6, where E_2 and E_6 are respectively the Eisenstein series A006352 and A013973.

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%I A386814 #4 Aug 03 2025 16:07:49
%S A386814 1,-600,34920,-157920,-23913240,297457776,3581091360,-13666238400,
%T A386814 -458367407640,-4230394757880,-25457298127632,-118465178148000,
%U A386814 -459399324219360,-1550209298287440,-4682236500918720,-12910757263315776,-32979872278342680,-78921341989665840,-178491991660958520
%N A386814 Coefficients in q-expansion of E_2^4 * E_6, where E_2 and E_6 are respectively the Eisenstein series A006352 and A013973.
%t A386814 terms = 20;
%t A386814 E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
%t A386814 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t A386814 CoefficientList[Series[E2[x]^4*E6[x], {x, 0, terms}], x]
%Y A386814 Cf. A006352, A013973, A386785.
%K A386814 sign
%O A386814 0,2
%A A386814 _Vaclav Kotesovec_, Aug 03 2025