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%I #16 Mar 05 2018 06:16:28
%S 1,-240,55440,-12793920,2952385680,-681306078240,157221316739520,
%T -36281112432850560,8372395974330234000,-1932052510261208053680,
%U 445849302141400152457440,-102886230661038692118348480
%N Expansion of reciprocal of theta series of E_8 lattice.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 123.
%H Seiichi Manyama, <a href="/A001943/b001943.txt">Table of n, a(n) for n = 0..422</a>
%F a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n), where c = 512 * Pi^12 / (9 * Gamma(1/3)^18) = 1.0411095643149212575756525710182812978684243780094495837147096816494... - _Vaclav Kotesovec_, Jul 02 2017, updated Mar 05 2018
%t terms = 12; s = 1/(1 + 240*Sum[k^3*(q^k/(1 - q^k)), {k, 1, terms}]) + O[q]^terms; CoefficientList[s, q] (* _Jean-François Alcover_, Jul 04 2017 *)
%Y Cf. A004009.
%K sign
%O 0,2
%A _N. J. A. Sloane_
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