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A045479
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McKay-Thompson series of class 2B for the Monster group with a(0) = -8.
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7
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1, -8, 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
| -1,2
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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.
The value of a(0) is the Rademacher constant for the modular function and appears in Conway and Norton's Table 4. - Michael Somos Mar 08 2011
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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).
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.
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LINKS
| T. D. Noe, Table of n, a(n) for n=-1..1000
Index entries for McKay-Thompson series for Monster simple group
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).
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FORMULA
| Expansion of 16 + (eta(q) / eta(q^2))^24 in powers of q. - Michael Somos Mar 08 2011
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EXAMPLE
| 1/q - 8 + 276*q - 2048*q^2 + 11202*q^3 - 49152*q^4 + 184024*q^5 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( 16 * x + (eta(x + A) / eta(x^2 + A))^24, n))} /* Michael Somos Mar 08 2011 */
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CROSSREFS
| A134786, A045479, A007191, A097340, A035099, A007246, A107080 are all essentially the same sequence.
Sequence in context: A098275 A129424 A159496 * A179570 A201188 A079929
Adjacent sequences: A045476 A045477 A045478 * A045480 A045481 A045482
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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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