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A244525
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Expansion of f(-x^1, -x^7) in powers of x where f(, ) is Ramanujan's general theta function.
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4
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1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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LINKS
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FORMULA
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Euler transform of period 8 sequence [-1, 0, 0, 0, 0, 0, -1, -1, ...].
G.f.: f(-x, -x^7) = Sum_{k in Z} (-1)^k * x^(4*k^2 - 3*k).
G.f.: Product_{k>0} (1 - x^(8*k-1)) * (1 - x^(8*k-7)) * (1 - x^(8*k)). - Seiichi Manyama, Jun 14 2016
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EXAMPLE
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G.f. = 1 - x - x^7 + x^10 + x^22 - x^27 - x^45 + x^52 + x^76 - x^85 + ...
G.f. = q^9 - q^25 - q^121 + q^169 + q^361 - q^441 - q^729 + q^841 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x^1, x^8] QPochhammer[ x^7, x^8] QPochhammer[ x^8], {x, 0, n}];
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PROG
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(PARI) {a(n) = issquare(16*n + 9) * (-1)^n};
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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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