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A107064
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Expansion of q^(-17/24) * (eta(q) * eta(q^6)^4) / (eta(q^2) * eta(q^3)^2) in powers of q.
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2
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1, -1, 0, 1, -1, -1, 0, 0, 0, 1, -1, 1, 0, 0, -1, 0, 1, 1, 1, 0, 0, -1, 0, -1, -1, 1, 1, 0, 0, 0, 0, -1, 0, -1, 1, -1, -1, 0, 1, -1, 1, 0, -1, 1, 0, 1, 0, 0, 0, 1, -1, -2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, -1, 0, -1, 0, -2, 0, 1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, -1, 1, 0, -1, -1, 0, 0, 1, 0, -1, -1, 0, 0, 0, 1, 1, 1, 0, 0, 0
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OFFSET
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0,52
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COMMENTS
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Ramanujan theta functions: f(q) := Product_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A010054), chi(q) := Product_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
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FORMULA
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Euler transform of period 6 sequence [ -1, 0, 1, 0, -1, -2, ...].
G.f.: Product_{k>0} ((1-x^(6k))(1+x^(3k)))^2/(1+x^k).
Expansion of psi(q^3)^2 * chi(-q) in powers of q where psi(), chi() are Ramanujan theta functions.
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-17/24)*(eta[q]*eta[q^6]^4)/(eta[q^2]*eta[q^3]^2), {q, 0, 100}], q] (* G. C. Greubel, Apr 18 2018 *)
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PROG
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^6 + A)^4 / eta(x^2 + A) / eta(x^3 + A)^2, 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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