OFFSET
0,19
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of q^(1/3)*(eta(q)*eta(q^6)*eta(q^10)*eta(q^15))/(eta(q^2) *eta(q^3)*eta(q^5)*eta(q^30)) in powers of q. - G. C. Greubel, Jun 06 2018
a(n) ~ (-1)^n * exp(2*Pi*sqrt(n/5)/3) / (2 * sqrt(3) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018
EXAMPLE
T90b = 1/q - q^2 - q^20 + q^23 - q^32 + q^35 - q^38 + q^41 - q^50 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(1/3)* (eta[q]*eta[q^6]*eta[q^10]*eta[q^15])/(eta[q^2]*eta[q^3]*eta[q^5]* eta[q^30]), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Mar 04 2018 *)
nmax = 100; CoefficientList[Series[Product[(1 - x^(2*k - 1))*(1 - x^(30*k - 15))/((1 - x^(6*k - 3))*(1 - x^(10*k - 5))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 29 2018 *)
PROG
(PARI) q='q+O('q^80); F=(eta(q)*eta(q^6)*eta(q^10)*eta(q^15))/(eta(q^2) *eta(q^3)*eta(q^5)*eta(q^30)); Vec(F) \\ G. C. Greubel, Jun 06 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Aug 28 2005
STATUS
approved