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A258277
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Expansion of chi(-q) * phi(-q^3) * psi(q^3) in powers of q where chi(), phi(), psi() are Ramanujan theta functions.
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15
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1, -1, 0, -2, 2, -1, 0, 0, 3, 0, 0, -2, 2, -2, 0, 0, 1, -2, 0, -2, 2, -1, 0, 0, 2, 0, 0, -2, 4, 0, 0, 0, 2, -3, 0, -2, 2, 0, 0, 0, 1, 0, 0, -4, 0, -2, 0, 0, 4, -2, 0, 0, 2, -2, 0, 0, 3, 0, 0, -2, 2, 0, 0, 0, 2, -1, 0, -2, 4, -2, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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Expansion of q^(-1/3) * eta(q) * eta(q^3) * eta(q^6) / eta(q^2) in powers of q.
Euler transform of period 6 sequence [ -1, 0, -2, 0, -1, -2, ...].
G.f.: Product_{k>0} (1 - x^(3*k)) * (1 - x^(6*k)) / (1 + x^k).
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EXAMPLE
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G.f. = 1 - x - 2*x^3 + 2*x^4 - x^5 + 3*x^8 - 2*x^11 + 2*x^12 - 2*x^13 + ...
G.f. = q - q^4 - 2*q^10 + 2*q^13 - q^16 + 3*q^25 - 2*q^34 + 2*q^37 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x^3] QPochhammer[ x^6] / QPochhammer[ -x, x], {x, 0, n}];
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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 + A) * eta(x^3 + A) * eta(x^6 + A) / eta(x^2 + 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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