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

%I #12 Feb 27 2018 02:57:35

%S 1,-1272,351432,89559456,-28689603384,-3415837464144,-155926897275744,

%T -3967939206760128,-65540990858009400,-777517458842153496,

%U -7105797244669716432,-52584588767807410464,-326903749149928526688,-1755591468945924647184

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

%H Seiichi Manyama, <a href="/A282328/b282328.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EisensteinSeries.html">Eisenstein Series.</a>

%t terms = 14;

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

%Y Cf. A004009 (E_4), A013973 (E_6).

%Y Cf. A013974 (E_4*E_6 = E_10), A282287 (E_4*E_6^2), this sequence (E_4*E_6^3).

%K sign

%O 0,2

%A _Seiichi Manyama_, Feb 12 2017