A001943 Expansion of reciprocal of theta series of E_8 lattice.

1, -240, 55440, -12793920, 2952385680, -681306078240, 157221316739520, -36281112432850560, 8372395974330234000, -1932052510261208053680, 445849302141400152457440, -102886230661038692118348480

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 123.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..422

Crossrefs

Cf. A004009.

Programs

Mathematica

terms = 12; s = 1/(1 + 240*Sum[k^3*(q^k/(1 - q^k)), {k, 1, terms}]) + O[q]^terms; CoefficientList[s, q] (* Jean-François Alcover, Jul 04 2017 *)

Formula

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n), where c = 512 * Pi^12 / (9 * Gamma(1/3)^18) = 1.0411095643149212575756525710182812978684243780094495837147096816494... - Vaclav Kotesovec, Jul 02 2017, updated Mar 05 2018