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A145706
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Expansion of chi(-x^5) / chi(-x^2) in powers of x where chi() is a Ramanujan theta function.
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3
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1, 0, 1, 0, 1, -1, 2, -1, 2, -1, 3, -2, 4, -2, 5, -4, 6, -5, 8, -6, 11, -8, 13, -10, 16, -14, 20, -17, 24, -21, 31, -26, 37, -32, 44, -41, 54, -49, 64, -59, 79, -72, 94, -86, 111, -106, 132, -126, 156, -149, 187, -178, 219, -210, 257, -251, 302, -295, 352
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OFFSET
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0,7
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COMMENTS
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LINKS
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FORMULA
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Expansion of q^(1/8) * eta(q^4) * eta(q^5) / (eta(q^2) * eta(q^10)) in powers of q.
Euler transform of period 20 sequence [ 0, 1, 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 1, -1, 0, 0, 1, 0, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (1280 t)) = f(t) where q = exp(2 Pi i t).
G.f.: Product_{k>0} (1 - x^(10*k - 5)) / (1 - x^(4*k - 2)).
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EXAMPLE
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G.f. = 1 + x^2 + x^4 - x^5 + 2*x^6 - x^7 + 2*x^8 - x^9 + 3*x^10 - 2*x^11 + ...
G.f. = 1/q + q^15 + q^31 - q^39 + 2*q^47 - q^55 + 2*q^63 - q^71 + 3*q^79 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x^5, x^10] QPochhammer[ -x^2, x^2], {x, 0, n}]; (* Michael Somos, Sep 06 2015 *)
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PROG
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(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A) * eta(x^5 + A) / (eta(x^2 + A) * eta(x^10 + A)), 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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