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A182031
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Expansion of q^(-5/24) * (eta(q^3) * eta(q^6))^3 / (eta(q) * eta(q^2))^4 in powers of q.
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1
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1, 4, 18, 53, 163, 414, 1059, 2431, 5553, 11844, 25013, 50391, 100362, 193136, 367371, 680705, 1247247, 2238408, 3975218, 6941384, 12003156, 20465599, 34581525, 57737205, 95601892, 156665029, 254777220, 410580026, 657015874
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OFFSET
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0,2
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COMMENTS
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REFERENCES
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H.-C. Chan, On the Andrews-Schur proof of the Rogers-Ramanujan identities, Ramanujan J. 23 (2010), no. 1-3, 417-431. see p. 430 Theorem 7.
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LINKS
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FORMULA
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Expansion of (psi(x^3) * phi(-x^3))^3 / (psi(x) * phi(-x))^4 in powers of x where phi(), psi() are Ramanujan theta functions.
Euler transform of period 6 sequence [ 4, 8, 1, 8, 4, 2, ...].
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EXAMPLE
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1 + 4*x + 18*x^2 + 53*x^3 + 163*x^4 + 414*x^5 + 1059*x^6 + 2431*x^7 + ...
q^5 + 4*q^13 + 18*q^21 + 53*q^29 + 163*q^37 + 414*q^45 + 1059*q^53 + ...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-5/8)*(eta[q^3]*eta[q^6])^3/(eta[q]*eta[q^2])^4, {q, 0, 100}], q] (* G. C. Greubel, Apr 16 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^3 + A) * eta(x^6 + A))^3 / (eta(x + A) * eta(x^2 + A))^4, n))}
(PARI) q='q+O('q^99); Vec((eta(q^3)*eta(q^6))^3/(eta(q)*eta(q^2))^4) \\ Altug Alkan, Apr 16 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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