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A058100
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McKay-Thompson series of class 10D for the Monster group.
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2
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1, 0, 21, 62, 162, 378, 819, 1680, 3276, 6138, 11145, 19662, 33840, 57048, 94362, 153432, 245757, 388218, 605466, 933414, 1423614, 2149586, 3215844, 4769544, 7016572, 10243896, 14848809, 21378276, 30582360, 43484304, 61473438, 86428896
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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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G.f. is Fourier series of a weight 0 level 10 modular form. f(-1/ ( 10 t)) = f(t) where q = exp(2 Pi i t).
Expansion of -6 + ((eta(q^2)*eta(q^5))/(eta(q)*eta(q^10)))^6 in powers of q. - G. C. Greubel, May 05 2018
a(n) ~ exp(2*Pi*sqrt(2*n/5)) / (2^(3/4) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
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EXAMPLE
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T10D = 1/q + 21*q + 62*q^2 + 162*q^3 + 378*q^4 + 819*q^5 + 1680*q^6 + ...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[-6 + ((eta[q^2]*eta[q^5])/(eta[q]*eta[q^10]))^6, {q, 0, 50}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, May 05 2018 *)
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PROG
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(PARI) q='q+O('q^30); Vec(-6 + ((eta(q^2)*eta(q^5))/(eta(q)* eta(q^10)) )^6/q) \\ G. C. Greubel, May 05 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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