A056947 Theta series of nonexistent Niemeier lattice of Coxeter number 1.

1, 24, 195984, 16779168, 397998672, 4629497040, 34417510848, 187489533504, 814881802320, 2975548760568, 9486548517600, 27052958750688, 70486228096704, 169931081461008, 384163595996544, 820166650027200, 1668890114013264, 3249630946490544, 6096882726702288

Offset

0,2

References

J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, 1988.

Links

Andy Huchala, Table of n, a(n) for n = 0..20000

Formula

E_12(z)+(24h-c12)*D(12) where D(12) is unique cusp form of weight 12, c12=(2*Pi)^12/(zeta(12)*gamma(12)) and h=1.

a(n) = (A029828(n) - 48936*A000594(n))/691. - Andy Huchala, Jul 11 2021

Example

G.f.: 1 + 24*q + 195984*q^2 + 16779168*q^3 + ...

Prog

(Sage)
d = CuspForms(1, 12).0.q_expansion(20);
e =(eisenstein_series_qexp(12, 20, normalization='integral'))
list(e/691-(48936/691)*d) # Andy Huchala, Jul 10 2021

Crossrefs

Cf. A029828, A000594.

Sequence in context: A201495 A258924 A179268 * A305760 A048057 A305757

Adjacent sequences: A056944 A056945 A056946 * A056948 A056949 A056950

Keyword

nonn

Author

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 17 2000

Status

approved