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A100004 Theta series of Barnes-Wall lattice in 128 dimensions. 1
1, 0, 0, 0, 1260230400, 0, 211691822284800, 167823813692620800, 478913396715566841600, 800774658647826785894400, 611331534352048834410577920, 247750040775246869910100377600, 59524143410351572596837132825600, 9219467698757233237143045380505600, 982518868151763901368740969501491200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag.

LINKS

Andy Huchala, Table of n, a(n) for n = 0..1000

Index entries for sequences related to Barnes-Wall lattices

EXAMPLE

Theta series = 1+1260230400*q^8+211691822284800*q^12+167823813692620800*q^14+

478913396715566841600*q^16+800774658647826785894400*q^18+

611331534352048834410577920*q^20+247750040775246869910100377600*q^22+

59524143410351572596837132825600*q^24+9219467698757233237143045380505600*q^26+

982518868151763901368740969501491200*q^28+

75861944796267943358105372399071395840*q^30+

4424187851601897335090905879137082310400*q^32+

201630718820389821054181008698644837171200*q^34+

7386564136116987592917746020874575301836800*q^36+

222716047981438421360112524163657218025062400*q^38+O(q^40)

or in terms of e8 and the cusp form:

e8^16-3840*e8^13*delta+4942080*e8^10*delta^2-2416128000*e8^7*delta^3

+364791398400*e8^4*delta^4-8259045949440*e8*delta^5.

PROG

(Sage) e8 = eisenstein_series_qexp(4, 25, normalization = "integral");

delta = CuspForms(1, 12).0.q_expansion(25);

f = e8^16-3840*e8^13*delta+4942080*e8^10*delta^2-2416128000*e8^7*delta^3+364791398400*e8^4*delta^4-8259045949440*e8*delta^5;

f[:25]

CROSSREFS

Sequence in context: A187565 A204606 A104966 * A113641 A186909 A288089

Adjacent sequences:  A100001 A100002 A100003 * A100005 A100006 A100007

KEYWORD

nonn

AUTHOR

Eric Rains and N. J. A. Sloane, Sep 27 2005

STATUS

approved

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Last modified December 1 16:29 EST 2021. Contains 349430 sequences. (Running on oeis4.)