A023922 Theta series of A*_10 lattice.

1, 0, 0, 0, 0, 22, 0, 0, 0, 110, 0, 110, 330, 0, 660, 924, 990, 0, 0, 0, 2662, 0, 1980, 4840, 0, 6534, 7260, 9460, 0, 0, 0, 15840, 0, 10230, 21780, 0, 27830, 32670, 33660, 0, 0, 0, 50820, 0, 30140, 71236, 0, 84700, 87120, 99000, 0, 0, 0, 136840, 0

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			G.f. = 1 + 22*q^5 + 110*q^9 + 110*q^11 + 330*q^12 + ... - _Sean A. Irvine_, Jun 16 2019
		

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 114.

Links

• G. Nebe and N. J. A. Sloane, Home page for this lattice
• K. Ono, On the Circular Summation of the Eleventh Powers of Ramanujan's Theta Function, Journal of Number Theory, Volume 76, Issue 1, May 1999, Pages 62-65.

Formula

G.f.: eta^11(q)/eta(q^11) + 800*q^5*eta^11(q^11)/eta(11) - 9*P11(q)*eta^11(q) + (308/3)*A(q) + (22/3)*B(q), where P11(q) is the g.f. for A213256, A(q) is the g.f. for A065103, B(q) is the g.f. for A065099, and eta is the Dedekind eta function [from Ono]. - Sean A. Irvine, Jun 16 2019

Extensions

More terms from Sean A. Irvine, Jun 16 2019