A107658 Coefficients of 6th root of theta series of Coxeter-Todd lattice K_{12} (see A004010).

1, 0, 126, 672, -36288, -413280, 15087870, 275661792, -6846707322, -186737716704, 3093536396160, 126405712075104, -1274633447433024, -84873293805379968, 385697576191762044, 56246329449791661600, 31646424393253329408

Offset: 0

Author

N. J. A. Sloane and Michael Somos, Jun 07 2005

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..693
• 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.

Crossrefs

Cf. A004010.

Programs

Mathematica

terms = 17; QP = QPochhammer; s = ((QP[q]^18*(4 - 4*(1 + (9*q*QP[q^9]^3) / QP[q]^3)^3 + 3*(1 + (9*q*QP[q^9]^3)/QP[q]^3)^6))/(3*QP[q^3]^6))^(1/6) + O[q]^terms; CoefficientList[s, q] (* Jean-François Alcover, Jul 08 2017, after Michael Somos *)