OFFSET
-1,5
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, Comm. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of (T14B - 2)^(1/2), where T14B = A058503, in powers of q. - G. C. Greubel, Jun 18 2018
a(n) ~ -(-1)^n * exp(sqrt(2*n/7)*Pi) / (2^(5/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018
EXAMPLE
T28C = 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 = 100; e28C2:= (eta[q^2]* eta[q^14])^3/(eta[q]*eta[q^4]^2*eta[q^7]*eta[q^28]^2); T14B := -1 + e28C2 + 4/e28C2; a:= CoefficientList[Series[((q (T14B - 2) + O[q]^nmax // Normal /. {q -> q^2}) + O[q]^nmax)^(1/2) // Normal, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
Terms a(12) onward added by G. C. Greubel, Jun 18 2018
STATUS
approved