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A058589
McKay-Thompson series of class 24f for Monster.
2
1, -3, -1, -3, -2, -9, 2, -9, -1, -24, 0, -27, 5, -51, -3, -60, -4, -108, 6, -129, -3, -210, -4, -252, 12, -393, -8, -474, -10, -702, 16, -852, -9, -1224, -8, -1485, 29, -2070, -17, -2511, -22, -3429, 38, -4155, -20, -5556, -20, -6723, 61, -8856, -36, -10695, -44, -13878, 80, -16722, -43
OFFSET
-1,2
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of A - 3*q/A, where A = q^(1/2)*(eta(q^2)*eta(q^4))/(eta(q^6) *eta(q^12)), in powers of q. - G. C. Greubel, Jun 18 2018
EXAMPLE
T24f = 1/q - 3*q - q^3 - 3*q^5 - 2*q^7 - 9*q^9 + 2*q^11 - 9*q^13 - q^15 - ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^4])/( eta[q^6]*eta[q^12]); a:= CoefficientList[Series[A - 3*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 18 2018 *)
PROG
(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^4))/(eta(q^6) *eta(q^12)); Vec(A - 3*q/A) \\ 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