A288472 -id:A288472 - cp's OEIS frontend

A288989 Denominators of coefficients in expansion of E_14/E_12.

1, 691, 477481, 329939371, 227988105361, 157539780804451, 108859988535875641, 75222252078290067931, 51978576186098436940321, 35917196144594019925761811, 24818782535914467768701411401, 17149778732316897228172675278091

Offset: 0

Seiichi Manyama, Jun 21 2017

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

Seiichi Manyama, Table of n, a(n) for n = 0..200

Cf. A288472 (numerators).

Cf. A029828, A058550 (E_14).

terms = 12;
E14[x_] = 1 - 24*Sum[k^13*x^k/(1 - x^k), {k, 1, terms}];
E12[x_] = 1 + (65520/691)*Sum[k^11*x^k/(1 - x^k), {k, 1, terms}];
E14[x]/E12[x] + O[x]^terms // CoefficientList[#, x]& // Denominator (* Jean-François Alcover, Feb 26 2018 *)

A288990 Define the exponents b(1), b(2), ... such that E_12 is equal to (1-q)^b(1) (1-q^2)^b(2) (1-q^3)^b(3) ... . a(n) = b(n) * A288989(n).

Original entry on oeis.org

-65520, -90598009320, 442356959924880, 4181653887366701917080, -42458488603945952980072176, -254774947034575235293755006524520, 3880639008647135220484579615019041680, 17460929863645555627595091312548802016985880

Offset: 1

Seiichi Manyama, Jun 21 2017

sign

			b(1) = 24 + 1/1 * A008683(1/1) * A288472(1)/A288989(1) = 24 + 1/1 * (-82104/691) = -65520/691,
b(2) = 24 + 1/2 * (A008683(2/1) * A288472(1)/A288989(1) + A008683(2/2) * A288472(2)/A288989(2)) = 24 + 1/2 * (82104/691 - 181275671592/477481) = -90598009320/477481.

Cf. A288989.

Cf. A288968 (k=2), A110163 (k=4), A288851 (k=6), A288471 (k=8).

b(n) = a(n)/A288989(n) = 24 + (1/n) * Sum_{d|n} A008683(n/d) * A288472(d)/A288989(d).

cp's OEIS Frontend

A288989 Denominators of coefficients in expansion of E_14/E_12.

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