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%I #14 Jul 06 2017 02:52:00
%S 1,0,0,2184,44226,530712,-22289904,-1041080040,-23414482728,
%T 86664734520,22704271546320,824932708688088,10338270616438674,
%U -363177176817506688,-24534229526034608016,-614775613733783853624,-526997882017733986314,591470477348411755418688,24257417213770154760619728,384176112414487265101313448
%N Coefficients of 12th root of theta series of lattice in A004046.
%H Vincenzo Librandi, <a href="/A107657/b107657.txt">Table of n, a(n) for n = 0..200</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.
%t terms = 20; QP = QPochhammer; Q9 = (1 + (9*q*QP[q^9]^3)/QP[q]^3); s = (1/(3^(1/4)*QP[q^3]))*QP[q]^3*(-8 + 16*Q9^3 + 64*Q9^6 - 72*Q9^9 + 27*Q9^12)^(1/12) + O[q]^terms; CoefficientList[s, q] (* _Jean-François Alcover_, Jul 06 2017, after _Michael Somos_ *)
%Y Cf. A004046.
%K sign
%O 0,4
%A _N. J. A. Sloane_ and _Michael Somos_, Jun 07 2005
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