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%I #24 Jun 16 2018 18:36:10
%S 1,-66,-40392,-9009264,-3725341158,-1400292801072,-604993149612720,
%T -262280205541007808,-118717180239835505592,-54520207050101542651506,
%U -25525844887805197307977968,-12095360676632550886664063760,-5797006133905562955666277287792,-2803076705590018145443840156918512
%N G.f.: 4th root of Eisenstein series E_10 (cf. A013974).
%H Vaclav Kotesovec, <a href="/A110150/b110150.txt">Table of n, a(n) for n = 0..360</a>
%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%F a(n) ~ c * exp(2*Pi*n) / n^(5/4), where c = -3^(3/4) * Pi^(3/2) / (2^(15/4) * Gamma(3/4)^7) = -0.227361380713650977567497769428903183591275821407342369621... - _Vaclav Kotesovec_, Jul 02 2017, updated Mar 05 2018
%F G.f.: Sum_{k>=0} A004984(k) * (33*f(q))^k where f(q) is Sum_{k>=1} sigma_9(k)*q^k. - _Seiichi Manyama_, Jun 16 2018
%t nmax = 20; s = 10; CoefficientList[Series[(1 - 2*s/BernoulliB[s] * Sum[DivisorSigma[s - 1, k]*x^k, {k, 1, nmax}])^(1/4), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 02 2017 *)
%Y E_k^(1/4): A289392 (k=2), A289307 (k=4), A289326 (k=6), A289292 (k=8), this sequence (k=10), A289391 (k=14).
%Y Cf. A004984, A013974, A109817, A289294.
%K sign
%O 0,2
%A _N. J. A. Sloane_, Sep 15 2005
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