|
%I #21 Feb 26 2018 17:24:46
%S 1,216,-200232,-85500576,-11218984488,-499862636784,-11084671590048,
%T -152346382155072,-1474691273530920,-10921720940625672,
%U -65489246355989232,-331011680696545248,-1452954445366288032,-5665058572086302256,-19968589327695656256
%N Coefficients in q-expansion of E_4^3*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="/A282000/b282000.txt">Table of n, a(n) for n = 0..1000</a>
%F -28728 * A013965(n) = 43867 * a(n) - 9504000 * A037944(n) for n > 0.
%t terms = 15;
%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] + 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), this sequence (E_4^3*E_6), A282047 (E_4^4*E_6), A282048 (E_4^5*E_6).
%Y Cf. A013965, A037944, A281928.
%K sign
%O 0,2
%A _Seiichi Manyama_, Feb 05 2017
|
