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, Commun. Algebra 22, No. 13, 5175-5193 (1994).
David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum
FORMULA
Expansion of B + 1 + 1/B, where B = eta(q)*eta(q^10)*eta(q^14)*eta(q^35)/ (eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)), in powers of q. - G. C. Greubel, Jun 30 2018
a(n) ~ exp(2*Pi*sqrt(2*n/35)) / (2^(3/4) * 35^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 30 2018
EXAMPLE
T70A = 1/q + q + 2*q^3 + 2*q^4 + 2*q^5 + 2*q^6 + 3*q^7 + 2*q^8 + 4*q^9 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; B:= eta[q]*eta[q^10]*eta[q^14]* eta[q^35]/(eta[q^2]*eta[q^5]*eta[q^7]*eta[q^70]); a:= CoefficientList[ Series[1 + B + 1/B, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 30 2018 *)
PROG
(PARI) q='q+O('q^50); B = eta(q)*eta(q^10)*eta(q^14)*eta(q^35)/ (q*eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)); Vec(B + 1 + 1/B) \\ G. C. Greubel, Jun 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 24 2014
STATUS
approved