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%I #26 Jun 14 2018 16:43:12
%S 1,0,8190,698880,-754790400,-131455134720,90235527782400,
%T 25034722952279040,-11631379080860106750,-4740180695347850188800,
%U 1500620323887236434821120,888527739621938585682240000,-181995668700704689414022799360,-164466129435036361896228722795520
%N Coefficients of series whose 24th power is the theta series of the Leech lattice (see A008408).
%D N. J. A. Sloane, Seven Staggering Sequences, in Homage to a Pied Puzzler, E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters, Wellesley, MA, 2009, pp. 93-110.
%H Seiichi Manyama, <a href="/A108093/b108093.txt">Table of n, a(n) for n = 0..378</a>
%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="https://dx.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.
%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. J. A. Sloane, <a href="http://neilsloane.com/doc/g4g7.pdf">Seven Staggering Sequences</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LeechLattice.html">Leech Lattice</a>
%e More precisely, the theta series of the Leech lattice (A008408) begins 1 + 196560*q^4 + 16773120*q^6 + 398034000*q^8 + 4629381120*q^10 + ... and the 24th root of this is 1 + 8190*q^4 + 698880*q^6 - 754790400*q^8 - 131455134720*q^10 + ...
%t terms = 14; s = (-45/16 EllipticTheta[2, 0, q]^8 EllipticTheta[3, 0, q]^8 EllipticTheta[4, 0, q]^8 + 1/8 (EllipticTheta[2, 0, q]^8 + EllipticTheta[3, 0, q]^8 + EllipticTheta[4, 0, q]^8)^3)^(1/24) + O[q]^(2 terms); (* _Jean-François Alcover_, Jul 07 2017, from LatticeData(Leech) *)
%Y Cf. A008408.
%K sign
%O 0,3
%A _N. J. A. Sloane_ and _Michael Somos_, Jun 06 2005
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