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

%I #17 Feb 27 2018 04:57:06

%S 1,-792,-197208,180534816,34731625896,-11282282306064,

%T -3475192229286624,-319729598062193088,-15436589476561121880,

%U -469831003553540798136,-9973761497118317484432,-158213220814147434639264,-1972935965978751882433248

%N Coefficients in q-expansion of E_4^3*E_6^3, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.

%H Seiichi Manyama, <a href="/A282461/b282461.txt">Table of n, a(n) for n = 0..1000</a>

%t terms = 13;

%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]^3* E6[x]^3 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 27 2018 *)

%Y Cf. A013974 (E_4*E_6 = E_10), A282292 (E_4^2*E_6^2 = E_10^2), this sequence (E_4^3*E_6^3 = E_10^3).

%K sign

%O 0,2

%A _Seiichi Manyama_, Feb 16 2017