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A007243
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McKay-Thompson series of class 3A for the Monster group with a(0) = 0.
(Formerly M5480)
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5
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1, 0, 783, 8672, 65367, 371520, 1741655, 7161696, 26567946, 90521472, 288078201, 864924480, 2469235686, 6748494912, 17746495281, 45086909440, 111066966315, 266057139456, 621284327856, 1417338712800, 3164665156308
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OFFSET
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-1,3
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COMMENTS
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Expansion of Hauptmodul for X_0^{+}(3).
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) ~ exp(4*Pi*sqrt(n/3)) / (sqrt(2) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 01 2017
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EXAMPLE
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T3A = 1/q + 783*q + 8672*q^2 + 65367*q^3 + 371520*q^4 + 1741655*q^5 + ...
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MATHEMATICA
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QP = QPochhammer; A = q*O[q]^20; A = (QP[q^3+A]/QP[q+A])^12; s = (1+27*q* A)^2/A - 42*q; CoefficientList[s, q] (* Jean-François Alcover, Nov 12 2015, adapted from PARI *)
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PROG
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(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x^3 + A) / eta(x + A))^12; polcoeff( (1 + 27 * x * A)^2 / A - 42 * x, n))} /* Michael Somos, Feb 02 2012 */
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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