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A058685
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McKay-Thompson series of class 45a for Monster.
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2
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1, 0, -1, 1, 0, 1, 2, 0, 1, 2, 0, -1, 4, 0, 1, 4, 0, -1, 6, 0, -1, 7, 0, 2, 11, 0, 0, 12, 0, -2, 16, 0, 0, 19, 0, 1, 25, 0, -1, 29, 0, 2, 37, 0, 1, 44, 0, -5, 56, 0, 3, 65, 0, 2, 80, 0, -5, 94, 0, 4, 114, 0, -1, 133, 0, -4, 160, 0, 7, 187, 0, 0, 223, 0, -6, 258, 0, 3, 305, 0, 3, 353, 0, -6, 415, 0
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OFFSET
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-1,7
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REFERENCES
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D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
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LINKS
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FORMULA
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Expansion of eta(q^9)*eta(q^15) / (eta(q^3)*eta(q^45)) - eta(q^3)*eta(q^45) / (eta(q^9)*eta(q^15)) in powers of q. - G. A. Edgar, Mar 20 2017
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EXAMPLE
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T45a = 1/q - q + q^2 + q^4 + 2*q^5 + q^7 + 2*q^8 - q^10 + 4*q^11 + q^13 + ...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q*eta[q^9]*eta[q^15]/(eta[q^3] *eta[q^45]); a := CoefficientList[Series[A - q^2/A , {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)
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PROG
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(PARI) q='q+O('q^99); Vec(eta(q^9)*eta(q^15) / (eta(q^3)*eta(q^45)) - q^2 * eta(q^3)*eta(q^45) / (eta(q^9)*eta(q^15))) \\ Joerg Arndt, Mar 20 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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