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A108094
Coefficients of series whose 16th power is the theta series of the 16-dimensional Barnes-Wall lattice (see A008409).
2
1, 0, 270, 3840, -514080, -15413760, 1283087040, 62644907520, -3378279124350, -252933976704000, 8502815843769600, 1007506223570707200, -17757117956815481280, -3942183666885514421760, 14527133705347401150720, 15088544258811557869278720, 144818514010649047069497600
OFFSET
0,3
LINKS
N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006.
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.
EXAMPLE
More precisely, the theta series of the Barnes-Wall lattice begins 1 + 4320*q^2 + 61440*q^3 + 522720*q^4 + 2211840*q^5 + 8960640*q^6 + 23224320*q^7 + ... and the 16th root of this is 1 + 270*q^2 + 3840*q^3 - 514080*q^4 - 15413760*q^5 + 1283087040*q^6 + 62644907520*q^7 - ...
MATHEMATICA
f[q_] := 1/2 (EllipticTheta[2, 0, q]^16 + EllipticTheta[3, 0, q]^16 + EllipticTheta[4, 0, q]^16 + 30 EllipticTheta[2, 0, q]^8 EllipticTheta[3, 0, q]^8);
CoefficientList[f[q]^(1/16) + O[q]^17, q] (* Jean-François Alcover, Aug 17 2018 *)
CROSSREFS
Sequence in context: A028529 A109025 A028535 * A162007 A289136 A317476
KEYWORD
sign
AUTHOR
STATUS
approved