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A058571
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McKay-Thompson series of class 24A for Monster.
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2
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1, 3, 3, 7, 18, 21, 30, 57, 75, 104, 156, 207, 293, 411, 525, 712, 984, 1248, 1622, 2169, 2757, 3530, 4560, 5736, 7284, 9249, 11472, 14374, 18078, 22242, 27484, 34140, 41787, 51184, 62796, 76317, 92893, 112998, 136275, 164671
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Expansion of q^(1/2) * (eta(q^2)^6 * eta(q^6)^6 / (eta(q)^3 * eta(q^3)^3 * eta(q^4)^3 * eta(q^12)^3)) in powers of q. - G. A. Edgar, Mar 11 2017
a(n) ~ exp(sqrt(2*n/3)*Pi) / (2^(5/4)*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 12 2017
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EXAMPLE
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T24A = 1/q + 3*q + 3*q^3 + 7*q^5 + 18*q^7 + 21*q^9 + 30*q^11 + 57*q^13 + ...
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MATHEMATICA
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nmax = 60; CoefficientList[Series[Product[((1 + x^k)*(1 + x^(3*k)) / ((1 + x^(2*k))*(1 + x^(6*k))))^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 12 2017 *)
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PROG
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(PARI) q='q+O('q^66); Vec( (eta(q^2)^6 * eta(q^6)^6 / (eta(q)^3 * eta(q^3)^3 * eta(q^4)^3 * eta(q^12)^3)) ) \\ Joerg Arndt, Mar 11 2017
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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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