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A112191
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McKay-Thompson series of class 48f for the Monster group.
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1
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1, 1, -1, 1, 0, 1, 0, 1, 1, 0, -2, 1, 1, 1, -1, 2, 2, 2, -2, 1, 1, 2, -2, 2, 4, 3, -4, 4, 2, 4, -2, 4, 5, 4, -6, 5, 5, 6, -5, 7, 8, 7, -8, 7, 6, 8, -8, 9, 13, 12, -14, 13, 10, 14, -10, 14, 17, 14, -20, 17, 17, 19, -18, 22, 24, 24, -26, 24, 22, 26, -26, 29, 37, 34, -39, 38, 32, 40, -34, 42, 48, 44, -54, 49
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OFFSET
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0,11
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LINKS
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FORMULA
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EXAMPLE
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T48f = 1/q +q -q^3 +q^5 +q^9 +q^13 +q^15 -2*q^19 +q^21 +q^23 +...
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MATHEMATICA
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eta[q_] := q^(1/24) * QPochhammer[q]; nmax = 100; A := q * (eta[q^8] * eta[q^12]/(eta[q^4] * eta[q^24]))^3; T24d := A - q^2/A; mcKayThompson48f := CoefficientList[Series[(T24d + 2*q + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[mcKayThompson48f[[n]], {n, 50}] (* G. C. Greubel, Jul 01 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = (eta(q^8)*eta(q^12)/(eta(q^4)*eta(q^24)))^3; T24d = A - q^2/A; Vec(sqrt(T24d + 2*q)) \\ G. C. Greubel, Jul 01 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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