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A058675
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McKay-Thompson series of class 42a for Monster.
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2
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1, 0, 3, 3, 3, 6, 7, 6, 12, 16, 18, 24, 33, 33, 48, 57, 69, 87, 106, 117, 153, 181, 207, 258, 307, 345, 429, 496, 570, 681, 805, 906, 1083, 1252, 1425, 1671, 1934, 2190, 2562, 2929, 3327, 3840, 4400, 4953, 5727, 6500, 7335, 8388, 9521, 10686, 12198, 13775
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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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a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, May 30 2018
Expansion of A - q/A, where A = q^(1/2)*(eta(q^3)*eta(q^7)/(eta(q)* eta(q^21))), in powers of q. - G. C. Greubel, Jun 19 2018
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EXAMPLE
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T42a = 1/q + 3*q^3 + 3*q^5 + 3*q^7 + 6*q^9 + 7*q^11 + 6*q^13 + 12*q^15 + ...
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MATHEMATICA
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CoefficientList[Series[(QPochhammer[x^3]^2 * QPochhammer[x^7]^2 - x*QPochhammer[x]^2 * QPochhammer[x^21]^2) / (QPochhammer[x] * QPochhammer[x^3] * QPochhammer[x^7] * QPochhammer[x^21]), {x, 0, 100}], x] (* Vaclav Kotesovec, May 30 2018 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]*eta[q^7]/( eta[q]*eta[q^21])); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 19 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = (eta(q^3)*eta(q^7)/(eta(q)* eta(q^21))); Vec(A - q/A) \\ G. C. Greubel, Jun 19 2018
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CROSSREFS
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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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