Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #46 Jun 15 2018 15:01:59
%S 1,-42,-11088,-3774624,-1472710974,-617481728640,-270883381218912,
%T -122585272771463040,-56747118995519331456,-26727350506044696990762,
%U -12760853360973370821796320,-6159994719956314185540737376,-3000691311646502407278581263104,-1472883416501251994527873967792256
%N G.f.: 12th root of Eisenstein series E_6 (cf. A013973).
%H Seiichi Manyama, <a href="/A109817/b109817.txt">Table of n, a(n) for n = 0..367</a>
%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0509316">On the Integrality of n-th Roots of Generating Functions</a>, arXiv:math/0509316 [math.NT], 2005-2006.
%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="https://doi.org/10.1016/j.jcta.2006.03.018">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%F G.f.: Product_{n>=1} (1-q^n)^(A288851(n)/12). - _Seiichi Manyama_, Jul 02 2017
%F a(n) ~ c * exp(2*Pi*n) / n^(13/12), where c = -Gamma(1/4)^(10/3) * Gamma(1/3)^2 / (16 * 6^(1/12) * Pi^3 * Gamma(1/12)) = -0.079329971529325538458906713053582098... - _Vaclav Kotesovec_, Jul 02 2017, updated Mar 05 2018
%F a(0) = 1, a(n) = -(1/n)*Sum_{k=1..n} A299503(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Feb 27 2018
%F G.f.: Sum_{k>=0} A303055(k) * f(q)^k where f(q) is Sum_{k>=1} sigma_5(k)*q^k. - _Seiichi Manyama_, Jun 15 2018
%t nmax = 20; s = 6; CoefficientList[Series[(1 - 2*s/BernoulliB[s] * Sum[DivisorSigma[s - 1, k]*x^k, {k, 1, nmax}])^(1/12), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 02 2017 *)
%Y E_6^(k/12): this sequence (k=1), A289325 (k=2), A289326 (k=3), A289327 (k=4), A289328 (k=5), A289293 (k=6), A289345 (k=7), A289346 (k=8), A289347 (k=9), A289348 (k=10), A289349 (k=11).
%Y Cf. A001160, A013973, A288851, A299503, A303055.
%K sign
%O 0,2
%A _N. J. A. Sloane_, Sep 15 2005