OFFSET
0,3
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
a(n) ~ exp(4*Pi*sqrt(n)/(3*sqrt(7))) / (sqrt(6) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, May 30 2018
Expansion of (q*T21A)^(1/3), where T21A = A058563. - G. C. Greubel, Jun 20 2018
Expansion of q^(1/2)*(((eta(q^3)*eta(q^7))^2 - (eta(q)*eta(q^21))^2)/( eta(q)*eta(q^3)*eta(q^7)*eta(q^21)))^(2/3) in powers of q. - G. C. Greubel, Jun 20 2018
EXAMPLE
T63a = 1/q + 2*q^5 + 2*q^8 + q^11 + 2*q^14 + 3*q^17 + 2*q^20 + 4*q^23 + ...
MATHEMATICA
CoefficientList[Series[((QPochhammer[x^3]^2 * QPochhammer[x^7]^2 - x*QPochhammer[x]^2 * QPochhammer[x^21]^2) / (QPochhammer[x] * QPochhammer[x^3] * QPochhammer[x^7] * QPochhammer[x^21]))^(2/3), {x, 0, 100}], x] (* Vaclav Kotesovec, May 30 2018 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; nmax = 120; e21B := eta[q]*eta[q^3]/( eta[q^7]*eta[q^21]); T21A := 1 + e21B + 7/e21B; a:= CoefficientList[ Series[(q*T21A + O[q]^nmax)^(1/3), {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 20 2018 *)
PROG
(PARI) q='q+O('q^50); Vec((((eta(q^3)*eta(q^7))^2 - q*(eta(q)*eta(q^21) )^2)/(eta(q)*eta(q^3)*eta(q^7)*eta(q^21)))^(2/3)) \\ G. C. Greubel, Jun 20 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 28 2005
STATUS
approved