A004534 Theta series of {D_14}^{+} lattice.

1, 0, 0, 0, 364, 0, 0, 8192, 16044, 0, 0, 114688, 200928, 0, 0, 745472, 1089452, 0, 0, 3096576, 4196920, 0, 0, 9691136, 12547808, 0, 0, 25346048, 31553344, 0, 0, 58261504, 70439852, 0, 0, 120553472, 142487436

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Crossrefs

Cf. A000122 (theta_3(q)), A002448 (theta_4(q)), A022045.

Formula

From Seiichi Manyama, Oct 21 2018: (Start)

Expansion of (theta_2(q)^14 + theta_3(q)^14 + theta_4(q)^14)/2 in powers of q^(1/2).

Expansion of (Sum_{k=-inf..inf} q^((k+1/2)^2))^14 + (Sum_{k=-inf..inf} q^(k^2))^14 + (Sum_{k=-inf..inf} (-1)^k * q^(k^2))^14 in powers of q^(1/2). (End)