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 + 2 + 4/A, where A = (eta(q)*eta(q^11)/(eta(q^2)*eta(q^22) ))^2, in powers of q. - G. C. Greubel, Jun 21 2018
a(n) ~ exp(2*Pi*sqrt(2*n/11)) / (2^(3/4) * 11^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
EXAMPLE
T22A = 1/q + 5*q + 6*q^2 + 16*q^3 + 20*q^4 + 41*q^5 + 50*q^6 + 97*q^7 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; A := (eta[q]*eta[q^11]/(eta[q^2]* eta[q^22]))^2; a:= CoefficientList[Series[q*(2 + A + 4/A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)
PROG
(PARI) q='q+O('q^50); A = (eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)))^2/q; Vec(A + 2 + 4/A) \\ G. C. Greubel, Jun 21 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 20 2014
STATUS
approved