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A058709
McKay-Thompson series of class 54a for Monster.
1
1, 0, 1, 1, 0, -1, 1, 0, 0, 2, 0, -1, 2, 0, 1, 3, 0, -1, 4, 0, 1, 5, 0, -1, 6, 0, 2, 7, 0, -1, 9, 0, 1, 11, 0, -2, 13, 0, 2, 16, 0, -2, 19, 0, 2, 23, 0, -3, 27, 0, 4, 32, 0, -3, 38, 0, 4, 44, 0, -5, 52, 0, 5, 61, 0, -6, 71, 0, 6, 82, 0, -7, 95, 0, 8, 110, 0, -8, 127, 0, 9, 145, 0, -9
OFFSET
-1,10
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of A + q^2/A, where A = q*(eta(q^6)*eta(q^27)/(eta(q^3)* eta(q^54))), in powers of q. - G. C. Greubel, Jun 27 2018
EXAMPLE
T54a = 1/q + q + q^2 - q^4 + q^5 + 2*q^8 - q^10 + 2*q^11 + q^13 + 3*q^14 - ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; A:= q*(eta[q^6]*eta[q^27]/(eta[q^3]* eta[q^54])); a:= CoefficientList[Series[A + q^2/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 27 2018 *)
PROG
(PARI) q='q+O('q^70); A = eta(q^6)*eta(q^27)/(eta(q^3)*eta(q^54)); Vec(A + q^2/A) \\ G. C. Greubel, Jun 27 2018
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
Terms a(24) onward added by G. C. Greubel, Jun 27 2018
STATUS
approved