A100004 Theta series of Barnes-Wall lattice in 128 dimensions.

1, 0, 0, 0, 1260230400, 0, 211691822284800, 167823813692620800, 478913396715566841600, 800774658647826785894400, 611331534352048834410577920, 247750040775246869910100377600, 59524143410351572596837132825600, 9219467698757233237143045380505600, 982518868151763901368740969501491200

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 * A366068 A113641 A186909

Adjacent sequences: A100001 A100002 A100003 * A100005 A100006 A100007

Keyword

nonn

Author

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

Status

approved