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A045489
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McKay-Thompson series of class 7A for the Monster group with a(0) = 3.
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4
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1, 3, 51, 204, 681, 1956, 5135, 12360, 28119, 60572, 125682, 251040, 487426, 920568, 1699611, 3070508, 5445510, 9490116, 16283793, 27537708, 45959775, 75760640, 123471327, 199081632, 317814988
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OFFSET
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-1,2
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LINKS
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FORMULA
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Expansion of -7 + (h+7)^2/h, where h = (eta(q)/eta(q^7))^4.
a(n) ~ exp(4*Pi*sqrt(n/7)) / (sqrt(2) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2017
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EXAMPLE
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1/q + 3 + 51*q + 204*q^2 + 681*q^3 + 1956*q^4 + 5135*q^5 + 12360*q^6 + ...
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MATHEMATICA
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QP = QPochhammer; h = q*(QP[q^7]/QP[q])^4; s = 1 - 7*q + q*((1+7*h)^2/h - 1/q) + O[q]^30; CoefficientList[s, q] (* Jean-François Alcover, Nov 15 2015 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; h:= (eta[q]/eta[q^7])^4; A045489 := CoefficientList[Series[q*(h + 7 + 49/h), {q, 0, 50}], q]; Table[ A045489[[n]], {n, 1, 30}] (* G. C. Greubel, May 28 2018 *)
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PROG
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(PARI) q='q+O('q^30); {h =(eta(q)/eta(q^7))^4/q}; Vec(h + 7 + 49/h) \\ G. C. Greubel, May 28 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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