OFFSET
0,5
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(T28B + 2) in powers of q, where T28B = A112169. - G. C. Greubel, Jul 01 2018
a(n) ~ exp(sqrt(2*n/7)*Pi) / (2^(5/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018
EXAMPLE
T56a = 1/q +q +q^3 +q^5 +3*q^7 +2*q^9 +2*q^11 +5*q^13 +6*q^15 +...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; nmax = 70; A:= (eta[q]*eta[q^7]/ (eta[q^4]*eta[q^28])); T28B := 1 + A + 4/A; a:= CoefficientList[Series[ (q*(T28B + 2) + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)
PROG
(PARI) q='q+O('q^50); A = eta(q)*eta(q^7)/(q*eta(q^4)*eta(q^28)); T28B = A + 1 + 4/A; Vec(sqrt(q*(T28B + 2))) \\ G. C. Greubel, Jul 01 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 28 2005
STATUS
approved