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^4)^4*eta(q^6)^4)/(eta(q)*eta(q^2)^2*eta(q^3) *eta(q^8)*eta(q^12)^2*eta(q^24)) in powers of q. - G. C. Greubel, Jun 18 2018
a(n) ~ exp(sqrt(2*n/3)*Pi) / (2^(5/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018
EXAMPLE
T24I = 1/q + 4*q + 6*q^2 + 11*q^3 + 18*q^4 + 28*q^5 + 42*q^6 + 62*q^7 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= (eta[q^4]^4*eta[q^6]^4)/(eta[q]* eta[q^2]^2*eta[q^3]*eta[q^8]*eta[q^12]^2*eta[q^24]); a:=CoefficientList[ Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)
PROG
(PARI) q='q+O('q^50); A = -1 + (eta(q^4)^4*eta(q^6)^4)/(eta(q)*eta(q^2)^2 *eta(q^3)*eta(q^8)*eta(q^12)^2*eta(q^24))/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