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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-Fran├žois 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

N. J. A. Sloane.

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 February 20 07:14 EST 2018. Contains 299359 sequences. (Running on oeis4.)