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 A002433 Theta series of unique 26-dimensional unimodular lattice T_26 with no roots (and minimal norm 3). 1
 1, 0, 0, 3120, 102180, 1482624, 13191360, 83859360, 416587860, 1712638720, 6061945344, 19019791440, 54048571200, 141266958720, 343675612800, 786321725280, 1706284712340, 3532676509440, 7012626150400, 13413721342320, 24829712546184, 44601384921600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES R. E. Borcherds, The Leech Lattice and Other Lattices, Ph. D. Dissertation, Cambridge Univ., 1984. J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, Third Ed., pp. xli-xlii. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..1000 N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745. FORMULA 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. EXAMPLE 1 + 3120*q^3 + 102180*q^4 + 1482624*q^5 + 13191360*q^6 + 83859360*q^7 + 416587860*q^8 + ... MATHEMATICA terms = 22; QP = QPochhammer; f = EllipticTheta[3, 0, q]; g = q*(QP[q]*(QP[q^4]/QP[q^2]))^8; s = f^26 - 52*f^18*g + 156*f^10*g^2 + O[q]^terms; CoefficientList[s, q] (* Jean-François Alcover, Jul 06 2017 *) CROSSREFS Sequence in context: A238513 A269324 A183850 * A107535 A181285 A133526 Adjacent sequences:  A002430 A002431 A002432 * A002434 A002435 A002436 KEYWORD nonn AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified January 23 06:15 EST 2019. Contains 319374 sequences. (Running on oeis4.)