A294183 - OEIS

%I #19 Jun 03 2018 08:05:30

%S 1,-984,393768,-129252576,38684099112,-10970838627984,

%T 3003345011096352,-801909012374388672,210169391033048138280,

%U -54295810529811041175672,13867098270790394508774768,-3508693915623201191415922848

%N Coefficients in expansion of E_6/E_8.

%H Seiichi Manyama, <a href="/A294183/b294183.txt">Table of n, a(n) for n = 0..421</a>

%F Convolution inverse of A288840.

%F a(n) ~ (-1)^n * 512 * Pi^12 * exp(Pi*sqrt(3)*n) * n / (3 * Gamma(1/3)^18). - _Vaclav Kotesovec_, Jun 03 2018

%t terms = 12;

%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];

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

%t E6[x]/E8[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 23 2018 *)

%Y Cf. A008410 (E_8). A013973 (E_6), A287933, A288840.

%Y E_k/E_{k+2}: A294181 (k=2), A294182 (k=4), this sequence (k=6).

%K sign

%O 0,2

%A _Seiichi Manyama_, Feb 11 2018