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).
David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum
FORMULA
Expansion of A - 1 + 1/A, where A = (eta(q^3)*eta(q^13)/(eta(q)* eta(q^39))), in powers of q. - G. C. Greubel, Jun 23 2018
a(n) ~ exp(4*Pi*sqrt(n/39)) / (sqrt(2) * 39^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018
EXAMPLE
T39A = 1/q + 3*q + q^2 + 3*q^3 + 6*q^4 + 6*q^5 + 9*q^6 + 15*q^7 + 15*q^8 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^3]*eta[q^13]/( eta[q]* eta[q^39])); a := CoefficientList[Series[A - 1 + 1/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)
PROG
(PARI) q='q+O('q^50); A = eta(q^3)*eta(q^13)/(q*eta(q)*eta(q^39)); Vec(A - 1 +1/A) \\ G. C. Greubel, Jun 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 20 2014
STATUS
approved