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Coefficients in q-expansion of E_4^5, where E_4 is the Eisenstein series shown in A004009.
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%I #21 Feb 26 2018 12:14:03

%S 1,1200,586800,148641600,20400279600,1439038231200,46093334702400,

%T 861697555612800,10894180752126000,102121497049868400,

%U 755966260027216800,4623420005167550400,24151632380348692800,110516281318431693600,451789183426135939200

%N Coefficients in q-expansion of E_4^5, where E_4 is the Eisenstein series shown in A004009.

%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="/A282015/b282015.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (1 + 240 Sum_{i>=1} i^3 q^i/(1-q^i))^5.

%F 13200 * A013967(n) = 174611 * a(n) - 209520000 * A037945(n) for n > 0.

%t terms = 15;

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

%t E4[x]^5 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)

%Y Cf. A004009 (E_4), A008410 (E_4^2), A008411 (E_4^3), A282012 (E_4^4), this sequence (E_4^5).

%Y Cf. A013967, A037945, A281788.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 05 2017