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A112189
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McKay-Thompson series of class 48d 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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refs;
listen;
history;
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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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T48d = 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^4]*eta[q^8]/ (eta[q^12]*eta[q^24])); T24g := A + 3*q^2/A; a:= CoefficientList[ Series[(T24g + 2*q + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 0, 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^4)*eta(q^8)/(eta(q^12)*eta(q^24)); T24g = A+ 3*q^2/A; Vec(sqrt(T24g + 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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