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Coefficients in expansion of 691*E_8*E_10*E_12.
2

%I #13 Feb 26 2018 10:18:46

%S 691,214776,10042488,-31595258016,-37453557900168,-14820419119618224,

%T -2593285239712936608,-222297419357081232192,-10663770067272328258440,

%U -324599563661107722245352,-6891830216922929182318512,-109326152051786546417315808

%N Coefficients in expansion of 691*E_8*E_10*E_12.

%H Seiichi Manyama, <a href="/A290049/b290049.txt">Table of n, a(n) for n = 0..1000</a>

%t terms = 12;

%t E8[x_] = 1 + 480*Sum[k^7*x^k/(1 - x^k), {k, 1, terms}];

%t E10[x_] = 1 - 264*Sum[k^9*x^k/(1 - x^k), {k, 1, terms}];

%t E12[x_] = 1 + (65520/691)*Sum[k^11*x^k/(1 - x^k), {k, 1, terms}];

%t 691*E8[x]*E10[x]*E12[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)

%Y Cf. A008410 (E_8), A013974 (E_10), A029828 (691*E_12).

%K sign

%O 0,1

%A _Seiichi Manyama_, Jul 19 2017