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A058674
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McKay-Thompson series of class 42D for Monster.
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1
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1, 0, 1, 3, 3, 4, 7, 7, 9, 15, 16, 20, 29, 32, 40, 55, 61, 74, 99, 111, 134, 170, 192, 230, 285, 323, 382, 466, 530, 622, 746, 848, 988, 1173, 1331, 1540, 1810, 2052, 2363, 2752, 3114, 3568, 4129, 4663, 5318, 6118, 6895, 7834, 8963, 10078, 11410, 12993, 14579
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OFFSET
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-1,4
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LINKS
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FORMULA
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Expansion of -1 + eta(q^2)*eta(q^6)*eta(q^7)*eta(q^21)/(eta(q)*eta(q^3) *eta(q^14)*eta(q^42)) in powers of q. - G. C. Greubel, Jun 24 2018
a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018
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EXAMPLE
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T42D = 1/q + q + 3*q^2 + 3*q^3 + 4*q^4 + 7*q^5 + 7*q^6 + 9*q^7 + 15*q^8 + ...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; A := ((eta[q^2]*eta[q^6]*eta[q^7] *eta[q^21])/(eta[q]*eta[q^3]*eta[q^14]*eta[q^42])); a:=CoefficientList[ Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 24 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = -1 + eta(q^2)*eta(q^6)*eta(q^7)*eta(q^21)/( eta(q)*eta(q^3)*eta(q^14)*eta(q^42))/q; Vec(A) \\ G. C. Greubel, Jun 24 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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