A109143 G.f.: cube root of theta series of E_6 lattice (cf. A004007).

1, 24, -486, 18960, -866028, 43409520, -2305522278, 127386486480, -7243559214894, 420974335099176, -24888628571711040, 1491922400816664432, -90454843306100805420, 5536766153219810009520, -341663245004722577661324, 21230836457057377337055600, -1327296238831338778081286796

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..540
• 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 = 17; QP = QPochhammer; s = (QP[q]^9/QP[q^3]^3 + 81 q QP[q^3]^9 / QP[q]^3)^(1/3) + O[q]^terms; CoefficientList[s, q] (* Jean-François Alcover, Jul 08 2017, after Michael Somos *)

Formula

a(n) ~ -(-1)^n * c * d^n / n^(4/3), where d = 68.1926041339304593440433078460708736926328270041397481947611089811133711468... and c = 0.241679782171000058724170446760823529819630243406508395073992160578... - Vaclav Kotesovec, Dec 11 2017