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Denominators of coefficients in expansion of E_14/E_12.
9

%I #17 Feb 26 2018 10:18:32

%S 1,691,477481,329939371,227988105361,157539780804451,

%T 108859988535875641,75222252078290067931,51978576186098436940321,

%U 35917196144594019925761811,24818782535914467768701411401,17149778732316897228172675278091

%N Denominators of coefficients in expansion of E_14/E_12.

%H Seiichi Manyama, <a href="/A288989/b288989.txt">Table of n, a(n) for n = 0..200</a>

%e E_14/E_12 = 1 - 82104/691 * q - 181275671592/477481 * q^2 + 1327007921039904/329939371 * q^3 + 16726528971891002133912/227988105361 * q^4 + ... .

%t terms = 12;

%t E14[x_] = 1 - 24*Sum[k^13*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 E14[x]/E12[x] + O[x]^terms // CoefficientList[#, x]& // Denominator (* _Jean-François Alcover_, Feb 26 2018 *)

%Y Cf. A288472 (numerators).

%Y Cf. A029828, A058550 (E_14).

%K nonn,frac

%O 0,2

%A _Seiichi Manyama_, Jun 21 2017