A109144 G.f.: cube root of theta series of E*_6 lattice (cf. A005129).

1, 0, 18, 24, -324, -720, 9234, 33696, -307926, -1614000, 10860480, 78618672, -385935492, -3854459520, 13226566500, 189101997360, -408244450788, -9247223107008, 9292147273170, 449330421257568, 41307157825920, -21633699079357296, -25580513164295232, 1028997388914059808

Offset: 0

Author

N. J. A. Sloane and Nadia Heninger, Aug 18 2005

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
• N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

Programs

Mathematica

terms = 24; QP = QPochhammer; s = ((QP[q]^3/QP[q^3])^3 + 9 q (QP[q^3]^3 / QP[q])^3)^(1/3) + O[q]^terms; CoefficientList[s, q] (* Jean-François Alcover, Jul 08 2017, after Michael Somos *)