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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

REFERENCES

R. Bacher and B. B. Venkov, Reseaux entiers unimodulaires sans racine en dimension 27 et 28, in Reseaux euclidiens, designs spheriques 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 edition.

LINKS

Table of n, a(n) for n=0..17.

R. Bacher and B. B. Venkov, Reseaux entiers unimodulaires sans racine en dimension 27 et 28 (html, ps).

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.

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

N. J. A. Sloane.

STATUS

approved

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Last modified March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)