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
Expansion of -1 + (eta(q^3)*eta(q^15))^2/(eta(q)*eta(q^5)*eta(q^9)* eta(q^45)) in powers of q. - G. C. Greubel, Jun 19 2018
a(n) ~ exp(4*Pi*sqrt(n/5)/3) / (5^(1/4) * sqrt(6) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018
EXAMPLE
T45A = 1/q + 2*q + q^2 + 3*q^3 + 4*q^4 + 5*q^5 + 6*q^6 + 7*q^7 + 11*q^8 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= (eta[q^3]*eta[q^15])^2/(eta[q] *eta[q^5]*eta[q^9]*eta[q^45]); a:= CoefficientList[Series[-1 + e45A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *)
PROG
(PARI) q='q+O('q^50); A = -1 + (eta(q^3)*eta(q^15))^2/(eta(q)*eta(q^5) *eta(q^9)*eta(q^45))/q; Vec(A) \\ G. C. Greubel, Jun 19 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 18 2014
STATUS
approved