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a(n) ~ exp(4*Pi*sqrt(n/39)) / (sqrt(2) * 39^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018
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eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*((eta[q^3]*eta[q^13])/(eta[q]*eta[q^39]) - 1), {q, 0, n60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018*)
(PARI) q='q+O('q^50); Vec((eta(q^3)*eta(q^13))/(q*eta(q)*eta(q^39)) - 1) \\ G. C. Greubel, Jun 19 2018
G. C. Greubel, <a href="/A058661/b058661.txt">Table of n, a(n) for n = -1..1000</a>
Expansion of -1 + (eta(q^3)*eta(q^13))/(eta(q)*eta(q^39)) in powers of q. - G. C. Greubel, Jun 19 2018
eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(eta[q^3]*eta[q^13])/(eta[q]*eta[q^39]) - 1), {q, 0, n}]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018*)
(PARI) q='q+O('q^50); Vec((eta(q^3)*eta(q^13))/(q*eta(q)*eta(q^39))) \\ G. C. Greubel, Jun 19 2018
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