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A058563
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McKay-Thompson series of class 21A for Monster.
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3
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1, 0, 6, 6, 15, 30, 41, 66, 111, 146, 222, 336, 463, 642, 942, 1238, 1698, 2334, 3090, 4098, 5514, 7136, 9336, 12216, 15673, 20142, 26013, 32880, 41820, 53070, 66609, 83568, 105039, 130482, 162321, 201708, 248802, 306642, 377955, 462596, 566223, 692064
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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(4*Pi*sqrt(n/21)) / (sqrt(2) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, May 30 2018
Expansion of A + 1 + 7/A, where A = eta(q)*eta(q^3)/(eta(q^7)*eta(q^21)), in powers of q. - G. C. Greubel, Jun 18 2018
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EXAMPLE
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T21A = 1/q + 6*q + 6*q^2 + 15*q^3 + 30*q^4 + 41*q^5 + 66*q^6 + 111*q^7 + ...
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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]))^2, {x, 0, 100}], x] (* Vaclav Kotesovec, May 30 2018 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= eta[q]*eta[q^3]/(eta[q^7] *eta[q^21]); a:= CoefficientList[Series[1 + A + 7/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = eta(q)*eta(q^3)/(q*eta(q^7)*eta(q^21)); Vec(A + 1 + 7/A) \\ G. C. Greubel, Jun 18 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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