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A002433
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Theta series of unique 26-dimensional unimodular lattice T_26 with no roots (and minimal norm 3).
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0
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1, 0, 0, 3120, 102180, 1482624, 13191360, 83859360, 416587860, 1712638720, 6061945344, 19019791440, 54048571200, 141266958720, 343675612800, 786321725280, 1706284712340, 3532676509440, 7012626150400, 13413721342320, 24829712546184, 44601384921600
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OFFSET
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0,4
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=0..21.
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.
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FORMULA
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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.
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EXAMPLE
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1 + 3120*q^3 + 102180*q^4 + 1482624*q^5 + 13191360*q^6 + 83859360*q^7 + 416587860*q^8 + ...
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CROSSREFS
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Sequence in context: A187593 A137839 A183850 * A107535 A181285 A133526
Adjacent sequences: A002430 A002431 A002432 * A002434 A002435 A002436
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar
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STATUS
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approved
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