OFFSET
0,9
COMMENTS
Also McKay-Thompson series of class 104B for Monster. - Michel Marcus, Feb 19 2014
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of sqrt(T52A) in powers of q, where T52A = A058705. - G. C. Greubel, Jul 02 2018
a(n) ~ exp(sqrt(2*n/13)*Pi) / (2^(5/4) * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018
EXAMPLE
T104A = 1/q +q^7 +q^11 +q^15 +q^23 +q^27 +2*q^31 +q^35 +2*q^39 +...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; B:= q^(1/2)*(eta[q^2]* eta[q^13]/(eta[q]*eta[q^26])); T52A:= B - q/B; a:= CoefficientList[ Series[(T52A + O[q]^nmax)^(1/2), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* G. C. Greubel, Jul 02 2018 *)
PROG
(PARI) q='q+O('q^70); B = (eta(q^2)*eta(q^13)/(eta(q)*eta(q^26))); Vec(sqrt(B - q/B)) \\ G. C. Greubel, Jul 02 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 28 2005
STATUS
approved