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A282047 Coefficients in q-expansion of E_4^4*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.

%I A282047 #18 Feb 26 2018 17:22:53
%S A282047 1,456,-146232,-133082976,-32170154808,-3378441902544,
%T A282047 -155862776255328,-3969266446940352,-65538944782146360,
%U A282047 -777506848190979672,-7105808014591457232,-52584752452485047328,-326903300701760852832,-1755591608260377411216
%N A282047 Coefficients in q-expansion of E_4^4*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
%D A282047 G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 208.
%H A282047 Seiichi Manyama, <a href="/A282047/b282047.txt">Table of n, a(n) for n = 0..1000</a>
%F A282047 -552 * A013969(n) = 77683 * a(n) - 35424000 * A037946(n) for n > 0.
%t A282047 terms = 14;
%t A282047 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A282047 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t A282047 E4[x]^4*E6[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)
%Y A282047 Cf. A004009 (E_4), A013973 (E_6), A013974 (E_4*E_6 = E_10), A058550 (E_4^2*E_6 = E_14), A282000 (E_4^3*E_6), this sequence (E_4^4*E_6), A282048 (E_4^5*E_6).
%Y A282047 Cf. A013969, A037946, A281956.
%K A282047 sign
%O A282047 0,2
%A A282047 _Seiichi Manyama_, Feb 05 2017