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A247223
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Expansion of f(-x^5, -x^7) in powers of x where f() is a Ramanujan theta function.
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5
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1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 0, -1, 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, 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 12 sequence [ 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, ...]. - Michael Somos, Jan 10 2015
G.f.: Product_{k>0} (1 - x^(12*k)) * (1 - x^(12*k - 5)) * (1 - x^(12*k - 7)).
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EXAMPLE
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G.f. = 1 - x^5 - x^7 + x^22 + x^26 - x^51 - x^57 + x^92 + x^100 - x^145 + ...
G.f. = q - q^121 - q^169 + q^529 + q^625 - q^1225 - q^1369 + q^2209 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[q^5, q^12]*QPochhammer[q^7, q^12] *QPochhammer[q^12, q^12], {q, 0, n}]; (* G. C. Greubel, dec 08 2017 *)
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PROG
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(PARI) {a(n) = my(m = 24*n + 1); if( issquare(m, &m) && (m%12==1 || m%12==11), (-1)^((m+6) \ 12))};
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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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