A008433 Theta series of {D_5}^{+} packing.

1, 0, 0, 0, 0, 16, 0, 0, 40, 0, 0, 0, 0, 80, 0, 0, 90, 0, 0, 0, 0, 160, 0, 0, 240, 0, 0, 0, 0, 240, 0, 0, 200, 0, 0, 0, 0, 400, 0, 0, 560, 0, 0, 0, 0, 496, 0, 0, 400, 0, 0, 0, 0, 560, 0, 0, 800, 0, 0, 0, 0, 880, 0, 0, 730

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			G.f.: 1 + 16*q^(5/4) + 40*q^2 + 80*q^(13/4) + 90*q^4 + ... .
		

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)), A005930.

Formula

From Seiichi Manyama, Oct 21 2018: (Start)

Expansion of (theta_2(q)^5 + theta_3(q)^5 + theta_4(q)^5)/2 in powers of q^(1/4).

Expansion of (Sum_{k=-oo..oo} q^((k+1/2)^2))^5 + (Sum_{k=-oo..oo} q^(k^2))^5 + (Sum_{k=-oo..oo} (-1)^k * q^(k^2))^5 in powers of q^(1/4). (End)