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%I #47 Mar 08 2018 06:40:30
%S -480,53520,-8192480,1417877520,-261761532384,50337746997520,
%T -9956715872256480,2010450258635669520,-412391756829925376480,
%U 85648872592091236716816,-17967933476075186380800480,3800832540589574135423637520
%N Exponents a(1), a(2), ... such that E_8, 1 + 480*q + 61920*q^2 + ... (A008410) is equal to (1-q)^a(1) (1-q^2)^a(2) (1-q^3)^a(3) ... .
%H Seiichi Manyama, <a href="/A288471/b288471.txt">Table of n, a(n) for n = 1..424</a>
%F a(n) = 16 + (2/(3*n)) * Sum_{d|n} A008683(n/d) * A288261(d).
%F a(n) = 2 * A110163(n) = 2 * A013953(n^2). - _Seiichi Manyama_, Jun 22 2017
%F a(n) = (1/n) * Sum_{d|n} A008683(n/d) * A289638(d). - _Seiichi Manyama_, Jul 09 2017
%F a(n) ~ 2 * (-1)^n * exp(Pi*sqrt(3)*n) / n. - _Vaclav Kotesovec_, Mar 08 2018
%Y Cf. A288968 (k=2), A110163 (k=4), A288851 (k=6), this sequence (k=8), A289024 (k=10), A288990/A288989 (k=12), A289029 (k=14).
%Y Cf. A008410 (E_8), A008683, A288261 (E_10/E_8), A289638.
%K sign
%O 1,1
%A _Seiichi Manyama_, Jun 21 2017
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