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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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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,3
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COMMENTS
| Expansion of Hauptmodul for X_0^{+}(3).
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REFERENCES
| J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
N. D. Elkies, Elliptic and modular curves..., in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 39.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters. Comm. Algebra 18 (1990), no. 1, 253-278.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Index entries for McKay-Thompson series for Monster simple group
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FORMULA
| a(n) = A030197(n) = A045480(n) unless n = 0.
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EXAMPLE
| T3A = 1/q + 783*q + 8672*q^2 + 65367*q^3 + 371520*q^4 + 1741655*q^5 + ...
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PROG
| (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
| Cf. A030197, A045480.
Sequence in context: A045074 A204279 A158399 * A146978 A095954 A187935
Adjacent sequences: A007240 A007241 A007242 * A007244 A007245 A007246
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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