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

Author

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

Keywords

• nonn

Examples

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

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

Crossrefs

Cf. A029828, A000594.

Programs

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

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