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

0,2

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.

Formula

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

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 *)

Crossrefs

Sequence in context: A159877 A319426 A275041 * A260964 A186863 A004383

Adjacent sequences: A109140 A109141 A109142 * A109144 A109145 A109146

Keyword

sign

Author

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

Status

approved