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A112160
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McKay-Thompson series of class 24E for the Monster group.
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6
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1, 4, 6, 8, 17, 28, 38, 56, 84, 124, 172, 232, 325, 448, 594, 784, 1049, 1388, 1796, 2320, 3005, 3864, 4912, 6216, 7877, 9940, 12430, 15488, 19309, 23972, 29580, 36408, 44766, 54876, 66978, 81536, 99150, 120272, 145374, 175344, 211242
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ exp(Pi*sqrt(2*n/3)) / (2 * 6^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015
Expansion of q^(1/6)*(eta(q^2)^2/(eta(q)*eta(q^4)))^4 in powers of q. - G. C. Greubel, Jan 25 2018
G.f.: exp(4*Sum_{k>=1} x^k/(k*(1 - (-x)^k))). - Ilya Gutkovskiy, Jun 07 2018
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EXAMPLE
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T24E = 1/q + 4*q^5 + 6*q^11 + 8*q^17 + 17*q^23 + 28*q^29 + 38*q^35 + ...
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MATHEMATICA
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nmax = 50; CoefficientList[Series[Product[(1 + x^(2*k+1))^4, {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)
eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(1/6)*(eta[q^2]^2/(eta[q]*eta[q^4]))^4, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jan 25 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = (eta(q^2)^2/(eta(q)*eta(q^4)))^4; Vec(A) \\ G. C. Greubel, Jul 01 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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STATUS
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approved
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