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A008697
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Theta series of Niemeier lattice of type A_8^3.
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4
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1, 216, 191376, 16827552, 397716048, 4630424400, 34416349632, 187486318656, 814898022480, 2975526941112, 9486526260960, 27053061396192, 70486156875456, 169930970535312, 384163673152896
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OFFSET
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0,2
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
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LINKS
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FORMULA
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This series is the q-expansion of (17*E_4(z)^3 + 7*E_6(z)^2)/24. - Daniel D. Briggs, Nov 25 2011
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MATHEMATICA
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terms = 15; E4[q_] := 1 + 240 Sum[DivisorSigma[3, n]*q^(2 n), {n, 1, terms}]; E6[q_] := 1 - 504 Sum[DivisorSigma[5, n]*q^(2 n), {n, 1, terms}]; s = 17/24 E4[q]^3 + 7/24 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-François Alcover, Jul 06 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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