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A112203
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McKay-Thompson series of class 60e for the Monster group.
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1
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1, 1, 0, 1, -1, 0, 1, 0, 0, 2, -1, 0, 2, 1, 0, 2, 0, 0, 3, 0, 0, 4, -1, 0, 4, 1, 0, 6, -1, 0, 7, 2, 0, 8, -2, 0, 10, 2, 0, 12, -2, 0, 14, 2, 0, 16, -1, 0, 19, 2, 0, 22, -3, 0, 26, 2, 0, 30, -3, 0, 35, 5, 0, 41, -5, 0, 47, 4, 0, 54, -5, 0, 62, 6, 0, 70, -4, 0, 80, 4, 0, 92, -7, 0, 104, 7, 0, 118, -7, 0, 135
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OFFSET
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0,10
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).
Index entries for McKay-Thompson series for Monster simple group
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FORMULA
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Expansion of A + q/A, where A = q^(1/2)*(eta(q^6)*eta(q^15)/( eta(q^3)* eta(q^30))), in powers of q. - G. C. Greubel, Jun 28 2018
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EXAMPLE
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T60e = 1/q +q +q^5 -q^7 +q^11 +2*q^17 -q^19 +2*q^23 +q^25 +...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^6]*eta[q^15]/( eta[q^3]*eta[q^30])); a:= CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 28 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = (eta(q^6)*eta(q^15)/(eta(q^3)*eta(q^30))); Vec(A + q/A) \\ G. C. Greubel, Jun 28 2018
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CROSSREFS
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Sequence in context: A095734 A137269 A112201 * A196279 A132798 A080425
Adjacent sequences: A112200 A112201 A112202 * A112204 A112205 A112206
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 28 2005
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STATUS
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approved
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