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A282012 Coefficients in q-expansion of E_4^4, where E_4 is the Eisenstein series shown in A004009.

%I A282012 #36 Feb 26 2018 19:20:11
%S A282012 1,960,354240,61543680,4858169280,137745912960,2120861041920,
%T A282012 21423820362240,158753769048000,928983317334720,4512174992346240,
%U A282012 18847874280625920,69518972236842240,230951926208599680,701949379778818560,1975788826748167680
%N A282012 Coefficients in q-expansion of E_4^4, where E_4 is the Eisenstein series shown in A004009.
%C A282012 Also coefficients in q-expansion of E_8^2.
%D A282012 G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 207.
%H A282012 Seiichi Manyama, <a href="/A282012/b282012.txt">Table of n, a(n) for n = 0..1000</a>
%F A282012 G.f.: (1 + 240 Sum_{i>=1} i^3 q^i/(1-q^i))^4.
%F A282012 16320 * A013963(n) = 3617 * a(n) - 3456000 * A027364(n) for n > 0.
%t A282012 terms = 16;
%t A282012 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A282012 E4[x]^4 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)
%Y A282012 Cf. A004009 (E_4), A008410 (E_4^2), A008411 (E_4^3), this sequence (E_4^4), A282015 (E_4^5).
%Y A282012 Cf. A281374 (E_2^2), A008410 (E_4^2), A280869 (E_6^2), this sequence (E_8^2), A282292 (E_10^2).
%Y A282012 Cf. A013963, A027364, A281876.
%K A282012 nonn
%O A282012 0,2
%A A282012 _Seiichi Manyama_, Feb 04 2017