A004532 Theta series of {D_10}^{+} lattice.

1, 0, 0, 0, 180, 512, 0, 0, 3380, 5120, 0, 0, 16320, 23040, 0, 0, 52020, 66560, 0, 0, 129064, 153600, 0, 0, 262080, 313344, 0, 0, 489600, 565760, 0, 0, 840500, 936960, 0, 0, 1330420, 1497600, 0, 0, 2050344, 2263040

Offset

0,5

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

Formula

From Seiichi Manyama, Oct 21 2018: (Start)

Expansion of (theta_2(q)^10 + theta_3(q)^10 + theta_4(q)^10)/2 in powers of q^(1/2).

Expansion of (Sum_{k=-inf..inf} q^((k+1/2)^2))^10 + (Sum_{k=-inf..inf} q^(k^2))^10 + (Sum_{k=-inf..inf} (-1)^k * q^(k^2))^10 in powers of q^(1/2). (End)

Crossrefs

Cf. A000122 (theta_3(q)), A002448 (theta_4(q), A008432.

Sequence in context: A015233 A307112 A211552 * A143793 A205818 A259312

Adjacent sequences: A004529 A004530 A004531 * A004533 A004534 A004535

Keyword

nonn

Author

N. J. A. Sloane

Status

approved