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A232714
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Expansion of f(-x, -x^6) in powers of x where f is Ramanujan's two-variable theta function.
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6
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1, -1, 0, 0, 0, 0, -1, 0, 0, 1, 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, -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, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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Euler transform of period 7 sequence [ -1, 0, 0, 0, 0, -1, -1, ...].
G.f.: Sum_{k in Z} (-1)^k * x^(k * (7*k + 5) / 2).
G.f.: Product_{k>0} (1 - x^(7*k-6)) * (1 - x^(7*k-1)) * (1 - x^(7*k)).
a(3*n + 2) = a(5*n + 2) = a(5*n + 3) = 0.
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EXAMPLE
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G.f. = 1 - x - x^6 + x^9 + x^19 - x^24 - x^39 + x^46 + x^66 - x^75 - x^100 + ...
G.f. = q^25 - q^81 - q^361 + q^529 + q^1089 - q^1369 - q^2209 + q^2601 + q^3721 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ SeriesCoefficient[ QPochhammer[ q, q^7] QPochhammer[ q^6, q^7] QPochhammer[ q^7], {q, 0, n}];
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PROG
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(PARI) {a(n) = my(m); if( issquare( 56*n + 25, &m), (-1)^round( m / 14), 0)};
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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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