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A108094
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Coefficients of series whose 16th power is the theta series of the 16-dimensional Barnes-Wall lattice (see A008409).
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2
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1, 0, 270, 3840, -514080, -15413760, 1283087040, 62644907520, -3378279124350, -252933976704000, 8502815843769600, 1007506223570707200, -17757117956815481280, -3942183666885514421760, 14527133705347401150720, 15088544258811557869278720, 144818514010649047069497600
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OFFSET
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0,3
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LINKS
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EXAMPLE
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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 - ...
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MATHEMATICA
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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);
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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