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A007246
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McKay-Thompson series of class 2B for Monster.
(Formerly M5434)
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9
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1, 0, 276, -2048, 11202, -49152, 184024, -614400, 1881471, -5373952, 14478180, -37122048, 91231550, -216072192, 495248952, -1102430208, 2390434947, -5061476352, 10487167336, -21301241856, 42481784514, -83300614144
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,3
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COMMENTS
| Unsigned sequence gives McKay-Thompson series of class 4A for Monster; also character of extremal vertex operator algebra of rank 12.
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REFERENCES
| J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
T. Gannon, Moonshine Beyond the Monster, Cambridge, 2006; see pp. 139, 424.
G. Hoehn, Selbstduale Vertexoperatorsuperalgebren und das Babymonster, Bonner Mathematische Schriften, Vol. 286 (1996), 1-85.
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
| T. D. Noe, Table of n, a(n) for n=-1..1000
R. E. Borcherds, Introduction to the monster Lie algebra, pp. 99-107 of M. Liebeck and J. Saxl, editors, Groups, Combinatorics and Geometry (Durham, 1990). London Math. Soc. Lect. Notes 165, Cambridge Univ. Press, 1992.
B. Brent, Quadratic Minima and Modular Forms, Experimental Mathematics, v.7 no.3, 257-274.
G. Hoehn (gerald(AT)math.ksu.edu), Selbstduale Vertexoperatorsuperalgebren und das Babymonster, Doctoral Dissertation, Univ. Bonn, Jul 15 1995 (pdf, ps).
Index entries for McKay-Thompson series for Monster simple group
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EXAMPLE
| T2B = 1/q + 276*q - 2048*q^2 + 11202*q^3 - 49152*q^4 + 184024*q^5 - ...
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CROSSREFS
| A134786, A045479, A007191, A097340, A035099, A007246, A107080 are all essentially the same sequence.
Sequence in context: A028532 A028522 * A107080 A169976 A166192 A186466
Adjacent sequences: A007243 A007244 A007245 * A007247 A007248 A007249
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KEYWORD
| sign,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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