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 A002482 Theta series of Borcherds' 27-dimensional unimodular lattice U_27. 0
 1, 0, 0, 2664, 101142, 1645056, 16045056, 110146176, 584713404, 2549741568, 9515943936, 31314087864, 92917622376, 252775586304, 638328674304, 1511740886400, 3387163161366, 7228598851584 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS R. Bacher and B. B. Venkov, Réseaux entiers unimodulaires sans racine en dimension 27 et 28, in Réseaux euclidiens, designs sphériques et formes modulaires, pp. 212-267, Enseignement Math., Geneva, 2001. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, Preface to 3rd ed. [alternative link] N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006; J. Combinatorial Theory, Series A, 113 (2006), 1732-1745. MAPLE th3^27-54*th3^19*delta8+216*th3^11*delta8^2 (th3 = A000122, delta8 = A002408). MATHEMATICA terms = 18; QP = QPochhammer; th3 = EllipticTheta[3, 0, q]; delta8 = q*(QP[q]*(QP[q^4]/QP[q^2]))^8; s = th3^27 - 54*th3^19*delta8 + 216*th3^11*delta8^2 + O[q]^terms; CoefficientList[s, q] (* Jean-François Alcover, Jul 06 2017 *) CROSSREFS Sequence in context: A197108 A224685 A167191 * A187293 A187195 A107532 Adjacent sequences:  A002479 A002480 A002481 * A002483 A002484 A002485 KEYWORD nonn AUTHOR STATUS approved

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Last modified June 28 05:40 EDT 2022. Contains 354903 sequences. (Running on oeis4.)