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A058516
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McKay-Thompson series of class 16C for Monster.
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4
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1, 0, 8, 16, 34, 64, 112, 192, 319, 512, 808, 1248, 1886, 2816, 4144, 6016, 8643, 12288, 17296, 24144, 33442, 45952, 62720, 85056, 114620, 153600, 204728, 271456, 358204, 470528, 615344, 801408, 1039621, 1343488, 1729920, 2219808, 2838920, 3619136, 4599664
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OFFSET
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-1,3
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COMMENTS
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LINKS
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FORMULA
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Expansion of eta(q^4)^10/(eta(q)^2 *eta(q^2)^3 *eta(q^8)^3* eta(q^16)^2)) - 2 in powers of q. - G. C. Greubel, May 28 2018
Expansion of -2 + (1/q) * chi(q)^2 * chi(q^2)^7 * chi(q^4)^2 in powers of q where chi() is a Ramanujan theta function. - Michael Somos, Feb 09 2019
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EXAMPLE
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T16C = 1/q + 8*q + 16*q^2 + 34*q^3 + 64*q^4 + 112*q^5 + 192*q^6 + 319*q^7 + ...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; A058516:= CoefficientList[Series[ q*(-2 + eta[q^4]^10/(eta[q]^2 *eta[q^2]^3 *eta[q^8]^3* eta[q^16]^2)), {q, 0, 60}], q]; Table[A058516[[n]], {n, 1, 50}] (* G. C. Greubel, May 28 2018 *)
a[ n_] := SeriesCoefficient[ -2 + q^-1 QPochhammer[ -q, q^2]^2 QPochhammer[ -q^2, q^4]^7 QPochhammer[ -q^4, q^8]^2, {q, 0, n}]; (* Michael Somos, Feb 09 2019 *)
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PROG
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(PARI) q='q+O('q^30); {h = (1/q)*(eta(q^4)^10/(eta(q)^2*eta(q^2)^3 *eta(q^8)^3*eta(q^16)^2))}; Vec(-2 + h) \\ G. C. Greubel, May 28 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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