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A058566
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McKay-Thompson series of class 21D for Monster.
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2
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1, 0, 5, 8, 16, 26, 44, 66, 104, 152, 229, 324, 469, 652, 916, 1250, 1716, 2306, 3108, 4116, 5464, 7156, 9373, 12144, 15725, 20190, 25889, 32952, 41881, 52904, 66716, 83688, 104785, 130608, 162486, 201336, 249006, 306874, 377482, 462860, 566513, 691404
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OFFSET
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-1,3
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LINKS
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FORMULA
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Expansion of -2 + (eta(q^3)*eta(q^7)/(eta(q)*eta(q^21)))^2 in powers of q. - G. C. Greubel, Jun 14 2018
a(n) ~ exp(4*Pi*sqrt(n/21)) / (sqrt(2) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
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EXAMPLE
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T21D = 1/q + 5*q + 8*q^2 + 16*q^3 + 26*q^4 + 44*q^5 + 66*q^6 + 104*q^7 + ...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-2 + (eta[q^3]*eta[q^7]/(eta[q]*eta[q^21]))^2), {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^50); A = -2+(eta(q^3)*eta(q^7)/(eta(q)*eta(q^21)))^2/q; Vec(A) \\ G. C. Greubel, Jun 14 2018
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CROSSREFS
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Cf. A226015 (same sequence except for n=0).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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