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%I #29 Jun 16 2018 12:32:41
%S 1,-6,-72,-1104,-20238,-405792,-8601840,-189317568,-4281478272,
%T -98841343686,-2318973049008,-55118876238000,-1324194430710912,
%U -32099173821105312,-784045854628721568,-19276683937074656064,-476644852188898489662
%N Coefficients in expansion of E_2^(1/4).
%H Seiichi Manyama, <a href="/A289392/b289392.txt">Table of n, a(n) for n = 0..702</a>
%F G.f.: Product_{n>=1} (1-q^n)^A289394(n).
%F a(n) ~ c / (n^(5/4) * r^n), where r = A211342 = 0.03727681029645165815098078565... is the root of the equation Sum_{k>=1} A000203(k) * r^k = 1/24 and c = -0.209452682241344640265132676904094736935029272937832600102950644347... - _Vaclav Kotesovec_, Jul 08 2017
%F G.f.: Sum_{k>=0} A004984(k) * (3*f(q))^k where f(q) is Sum_{k>=1} sigma_1(k)*q^k. - _Seiichi Manyama_, Jun 16 2018
%t nmax = 20; CoefficientList[Series[(1 - 24*Sum[DivisorSigma[1, k]*x^k, {k, 1, nmax}])^(1/4), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 08 2017 *)
%Y E_2^(k/4): this sequence (k=1), A289291 (k=2), A289393 (k=3).
%Y E_k^(1/4): this sequence (k=2), A289307 (k=4), A289326 (k=6), A289292 (k=8), A110150 (k=10), A289391 (k=14).
%Y Cf. A004984, A006352 (E_2), A108091, A109817, A289394.
%K sign
%O 0,2
%A _Seiichi Manyama_, Jul 05 2017
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