A055747 Expansion of Jacobi form of weight 12 and index 1 for the Niemeier lattice of type E_8^3 or D_16+E_8.

1, 0, 0, 56, 606, 0, 0, 27456, 123156, 0, 0, 3745512, 9217112, 0, 0, 95209152, 188066718, 0, 0, 1144371624, 1960489800, 0, 0, 8505838656, 13289979912, 0, 0, 45755357024, 67080028224, 0, 0, 195411318912, 272570040468, 0, 0

Offset: 0

Author

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 11 2000

Keywords

• nonn

Comments

a(4*n-r^2) gives number of vectors x in the lattice of norm 2n and =r for any fixed vector in the lattice of norm 2.

References

• M. Eichler and D. Zagier, The Theory of Jacobi Forms, Birkhauser, 1985.

Crossrefs

Cf. A008411, A003783, A004009.

Formula

E_8*E_4, 1.

G.f.: b(z) * c(z) where b(z) is g.f. for A003783 and c(z) = 1 + 240*z^4 + 2160*z^8 + ... is A004009 expanded in powers of z^4. - Sean A. Irvine, Apr 05 2022