OFFSET
-1,13
COMMENTS
Also McKay-Thompson series of class 78C for Monster. - Michel Marcus, Feb 19 2014
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).
FORMULA
Expansion of 1 + eta(q)*eta(q^6)*eta(q^26)*eta(q^39)/(eta(q^2)*eta(q^3) *eta(q^13)*eta(q^78)) in powers of q. - G. C. Greubel, Jun 19 2018
a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/39)) / (2 * 39^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018
EXAMPLE
T78B = 1/q - q^4 + q^5 - q^6 + q^7 - q^10 + 2*q^11 - q^12 + q^15 - 2*q^16 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= eta[q]*eta[q^6]*eta[q^26]* eta[q^39]/( eta[q^2]*eta[q^3]*eta[q^13]*eta[q^78]); a:= CoefficientList[Series[q*(1 + A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *)
PROG
(PARI) q='q+O('q^50); A = 1 + eta(q)*eta(q^6)*eta(q^26)*eta(q^39)/( eta(q^2)*eta(q^3)*eta(q^13)*eta(q^78))/q; Vec(A) \\ G. C. Greubel, Jun 19 2018
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 18 2014
STATUS
approved