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Coefficients in q-expansion of E_4^4, where E_4 is the Eisenstein series shown in A004009.
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%I #36 Feb 26 2018 19:20:11

%S 1,960,354240,61543680,4858169280,137745912960,2120861041920,

%T 21423820362240,158753769048000,928983317334720,4512174992346240,

%U 18847874280625920,69518972236842240,230951926208599680,701949379778818560,1975788826748167680

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

%C Also coefficients in q-expansion of E_8^2.

%D G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 207.

%H Seiichi Manyama, <a href="/A282012/b282012.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))^4.

%F 16320 * A013963(n) = 3617 * a(n) - 3456000 * A027364(n) for n > 0.

%t terms = 16;

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

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

%Y Cf. A004009 (E_4), A008410 (E_4^2), A008411 (E_4^3), this sequence (E_4^4), A282015 (E_4^5).

%Y Cf. A281374 (E_2^2), A008410 (E_4^2), A280869 (E_6^2), this sequence (E_8^2), A282292 (E_10^2).

%Y Cf. A013963, A027364, A281876.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 04 2017