OFFSET
0,6
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
a(n) ~ exp(Pi*sqrt(2*n)/3) / (2^(5/4)*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Nov 12 2015
Expansion of q^(1/2)*(eta(q^2)*eta(q^3)^2*eta(q^12)^2*eta(q^18)/(eta(q) *eta(q^4)*eta(q^6)^2*eta(q^9)*eta(q^36))) in powers of q. - G. C. Greubel, Jun 16 2018
EXAMPLE
T72a = 1/q + q + q^3 + q^7 + 2*q^9 + 2*q^11 + 2*q^13 + 3*q^15 + 4*q^17 + ...
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[(1+x^k) * (1-x^(3*k))^2 * (1+x^(6*k))^2 * (1+x^(9*k)) / ((1-x^(4*k)) * (1-x^(36*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 12 2015 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; e72a:= q^(1/2)*((eta[q^2]*eta[q^3]^2 *eta[q^12]^2*eta[q^18])/(eta[q]*eta[q^4]*eta[q^6]^2*eta[q^9]*eta[q^36])); a[n_]:= SeriesCoefficient[e72a, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 18 2018 *)
PROG
(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^3)^2*eta(q^12)^2*eta(q^18)/( eta(q)*eta(q^4)*eta(q^6)^2*eta(q^9)*eta(q^36))); Vec(A) \\ G. C. Greubel, Jun 16 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 28 2005
STATUS
approved