%I A002433
%S A002433 1,0,0,3120,102180,1482624,13191360,83859360,416587860,1712638720,6061945344,
%T A002433 19019791440,54048571200,141266958720,343675612800,786321725280,1706284712340,
%U A002433 3532676509440,7012626150400,13413721342320,24829712546184,44601384921600
%N A002433 Theta series of unique 26-dimensional unimodular lattice T_26 with no 
               roots (and minimal norm 3).
%D A002433 R. E. Borcherds, The Leech Lattice and Other Lattices, Ph. D. Dissertation, 
               Cambridge Univ., 1984.
%D A002433 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", 
               Springer-Verlag, Third Ed., pp. xli-xlii.
%H A002433 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.
%F A002433 Let f = theta_3, g = 8-dimensional cusp form [Conway-Sloane, p. 187, 
               Eqs. (32)-(34)]. The theta-series is f^26 - 52*f^18*g + 156*f^10*g^2.
%e A002433 1 + 3120*q^3 + 102180*q^4 + 1482624*q^5 + 13191360*q^6 + 83859360*q^7 
               + 416587860*q^8 + ...
%Y A002433 Sequence in context: A092129 A103523 A090056 this_sequence A107535 A133526 
               A102709
%Y A002433 Adjacent sequences: A002430 A002431 A002432 this_sequence A002434 A002435 
               A002436
%K A002433 nonn
%O A002433 0,4
%A A002433 N. J. A. Sloane (njas(AT)research.att.com).
%E A002433 Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 23 2008 at 
               the suggestion of R. J. Mathar