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A110163
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Exponents a(1), a(2), ... such that theta series of E_8 lattice, 1 + 240 q + 2160 q^2 + ... (A004009) is equal to (1-q)^a(1) (1-q^2)^a(2) (1-q^3)^a(3) ...
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23
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-240, 26760, -4096240, 708938760, -130880766192, 25168873498760, -4978357936128240, 1005225129317834760, -206195878414962688240, 42824436296045618358408, -8983966738037593190400240, 1900416270294787067711818760, -404814256845771786255876096240, 86744167089111545378556727322760
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OFFSET
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1,1
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COMMENTS
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Negative of inverse Euler transform of [240, 2160, ...].
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LINKS
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FORMULA
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EXAMPLE
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MATHEMATICA
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terms = 14; Clear[a, sol];
a4009[n_] := If[n == 0, 1, 240 DivisorSigma[3, n]];
sol[0] = {}; sol[kmax_] := sol[kmax] = Join[sol[kmax-1], SolveAlways[ Sum[ a4009[k] q^k, {k, 0, kmax}] == Normal[Product[(1-q^k)^a[k], {k, 1, kmax}] + O[q]^(kmax+1)] /. sol[kmax-1], q][[1]] ];
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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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