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Coefficients in q-expansion of E_4^4*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
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%I #18 Feb 26 2018 17:22:53

%S 1,456,-146232,-133082976,-32170154808,-3378441902544,

%T -155862776255328,-3969266446940352,-65538944782146360,

%U -777506848190979672,-7105808014591457232,-52584752452485047328,-326903300701760852832,-1755591608260377411216

%N 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 G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 208.

%H Seiichi Manyama, <a href="/A282047/b282047.txt">Table of n, a(n) for n = 0..1000</a>

%F -552 * A013969(n) = 77683 * a(n) - 35424000 * A037946(n) for n > 0.

%t terms = 14;

%t E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];

%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];

%t E4[x]^4*E6[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)

%Y 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 Cf. A013969, A037946, A281956.

%K sign

%O 0,2

%A _Seiichi Manyama_, Feb 05 2017