OFFSET
-1,3
LINKS
G. C. Greubel, Table of n, a(n) for n = -1..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(2*Pi*sqrt(2*n/15)) / (2^(3/4) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2017
Expansion of -1 + ((eta(q^3)*eta(q^5)*eta(q^6)*eta(q^10))/(eta(q)* eta(q^2)*eta(q^15)*eta(q^30))) in powers of q. - G. C. Greubel, Jun 18 2018
EXAMPLE
T30F = 1/q + 3*q + 3*q^2 + 8*q^3 + 8*q^4 + 16*q^5 + 17*q^6 + 33*q^7 + ...
MATHEMATICA
nmax = 50; CoefficientList[Series[-x + Product[(1 - x^(3*k))*(1 - x^(5*k))*(1 - x^(6*k))*(1 - x^(10*k))/((1 - x^k)*(1 - x^(2*k))*(1 - x^(15*k))*(1 - x^(30*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 07 2017 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= ((eta[q^3]*eta[q^5]*eta[q^6] *eta[q^10])/(eta[q]*eta[q^2]*eta[q^15]*eta[q^30])); a:= CoefficientList[Series[-1 + A, {q, 0, 60}], q]; Table[A058617[n], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)
PROG
(PARI) q='q+O('q^50); A = -1 + ((eta(q^3)*eta(q^5)*eta(q^6)*eta(q^10))/( eta(q)*eta(q^2)*eta(q^15)*eta(q^30)))/q; Vec(A) \\ G. C. Greubel, Jun 18 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 18 2014
STATUS
approved