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A112184
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McKay-Thompson series of class 44b for the Monster group.
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1
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1, -1, 0, -1, 1, -1, 1, -1, 2, -2, 2, -3, 4, -3, 4, -5, 6, -6, 6, -8, 9, -10, 10, -12, 14, -15, 16, -19, 21, -22, 24, -27, 31, -34, 36, -40, 46, -48, 52, -58, 64, -69, 74, -82, 91, -98, 104, -115, 127, -136, 145, -159, 174, -186, 200, -218, 238, -254, 272, -296, 322, -343, 366, -398, 430, -460, 492, -531
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OFFSET
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0,9
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LINKS
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FORMULA
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Expansion of q^(1/2)*(eta(q)*eta(q^11)/(eta(q^2)*eta(q^22))) in powers of q. - G. C. Greubel, Jun 28 2018
a(n) ~ (-1)^n * exp(sqrt(2*n/11)*Pi) / (2^(5/4) * 11^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018
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EXAMPLE
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T44b = 1/q -q -q^5 +q^7 -q^9 +q^11 -q^13 +2*q^15 -2*q^17 +...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q]*eta[q^11]/(eta[q^2]*eta[q^22])), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 28 2018 *)
nmax = 60; CoefficientList[Series[Product[(1 - x^(2*k-1))*(1 - x^(22*k-11)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 29 2018 *)
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PROG
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(PARI) q='q+O('q^50); Vec((eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)))) \\ G. C. Greubel, Jun 28 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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