OFFSET
0,13
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, Comm. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of sqrt(T66A) in powers of q, where T66A = A058739. - G. C. Greubel, Jul 03 2018
a(n) ~ exp(2*Pi*sqrt(n/33)) / (2 * 33^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 03 2018
EXAMPLE
T132a = 1/q +q^3 +q^9 +q^11 +q^15 +q^17 +q^19 +q^21 +2*q^23 +...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 120; b:= (eta[q^2]*eta[q^3]* eta[q^22]*eta[q^33])/(eta[q]*eta[q^6]*eta[q^11]*eta[q^66]); T66A:= -1 + b + 1/b; a:= CoefficientList[Series[(q*T66A + O[q]^nmax)^(1/2), {q, 0, 100}], q]; Table[a[[n]], {n, 1, 80}] (* G. C. Greubel, Jul 03 2018 *)
PROG
(PARI) q='q+O('q^80); b = (eta(q^2)*eta(q^3)* eta(q^22)*eta(q^33))/(q* eta(q)*eta(q^6)*eta(q^11)*eta(q^66)); T66A = b - 1 + 1/b; Vec(sqrt(q*T66A)) \\ G. C. Greubel, Jul 03 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 28 2005
STATUS
approved