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A101558
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McKay-Thompson series of class 2A for the Monster group.
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6
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1, 0, 4372, 96256, 1240002, 10698752, 74428120, 431529984, 2206741887, 10117578752, 42616961892, 166564106240, 611800208702, 2125795885056, 7040425608760, 22327393665024, 68134255043715, 200740384538624
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OFFSET
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-1,3
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COMMENTS
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Hauptmodul for Gamma_0(2)+.
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REFERENCES
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T. Gannon, Moonshine Beyond the Monster, Cambridge, 2006; see p. 423.
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = -1..10000
R. E. Borcherds, Review of "Moonshine Beyond the Monster ..." (Cambridge, 2006), Bull. Amer. Math. Soc., 45 (2008), 675-679.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006; J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
Index entries for McKay-Thompson series for Monster simple group
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FORMULA
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a(n) ~ exp(2*Pi*sqrt(2*n)) / (2^(3/4)*n^(3/4)). - Vaclav Kotesovec, Apr 01 2017
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EXAMPLE
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T2A = 1/q + 4372q + 96256q^2 + 1240002q^3 + ...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; f2A:= (eta[q]/eta[q^2])^24*(1 + 64*( eta[q^2]/eta[q])^24)^2; a:= CoefficientList[Series[q*(f2A - 104), {q, 0, 50}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, May 10 2018 *)
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PROG
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(PARI) {a(n) = my(A); if( n<-1, 0, A = prod(k=1, n\2+1, 1 - x^(2*k-1), 1 + x^2 * O(x^n))^24; polcoeff(64^2*x/A + A/x + 24, n))};
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CROSSREFS
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A045478, A007241, A106207, A007267, A101558 are all essentially the same sequence.
Cf. A007241 (same except for 0th term), A007267, A045478.
Sequence in context: A207047 A001378 A028511 * A163583 A203403 A206148
Adjacent sequences: A101555 A101556 A101557 * A101559 A101560 A101561
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Dec 06 2004
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STATUS
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approved
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