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%I #23 Mar 08 2018 06:41:27
%S 504,143388,51180024,20556578700,8806299845112,3929750661380124,
%T 1803727445909594616,845145871847732769804,402283166289266872824312,
%U 193877350835487271784566812,94381548697864188120110027256,46328820782943001597184984563596
%N Exponents a(1), a(2), ... such that E_6, 1 - 504*q - 16632*q^2 - ... (A013973) is equal to (1-q)^a(1) (1-q^2)^a(2) (1-q^3)^a(3) ... .
%H Seiichi Manyama, <a href="/A288851/b288851.txt">Table of n, a(n) for n = 1..367</a>
%H R. E. Borcherds, <a href="http://www.math.berkeley.edu/~reb/papers/">Automorphic forms on O_{s+2,2}(R)^{+} and generalized Kac-Moody algebras</a>, pp. 744-752 of Proc. Intern. Congr. Math., Vol. 2, 1994.
%F a(n) = A013975(n^2) for n>=1.
%F a(n) = 12 + (1/(2*n)) * Sum_{d|n} A008683(n/d) * A288840(d).
%F a(n) = (1/n) * Sum_{d|n} A008683(n/d) * A289637(d). - _Seiichi Manyama_, Jul 09 2017
%F a(n) ~ exp(2*Pi*n) / n. - _Vaclav Kotesovec_, Mar 08 2018
%Y Cf. A288968 (k=2), A110163 (k=4), this sequence (k=6), A288471 (k=8), A289024 (k=10), A288990/A288989 (k=12), A289029 (k=14).
%Y Cf. A008683, A013973 (E_6), A110163, A288840 (E_8/E_6), A289637.
%K nonn
%O 1,1
%A _Seiichi Manyama_, Jun 18 2017
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