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Search: id:A007266
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| A007266 |
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McKay-Thompson series of class 9A for Monster.
(Formerly M5192)
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+0
3
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| 1, 0, 27, 86, 243, 594, 1370, 2916, 5967, 11586, 21870, 39852, 71052, 123444, 210654, 352480, 581013, 942786, 1510254, 2388204, 3734964, 5777788, 8852004, 13434984, 20218395, 30177684, 44704413, 65743348, 96033357, 139368816
(list; graph; listen)
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OFFSET
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-1,3
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COMMENT
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G.f. A(x) satisfies 0=f(A(x)+6,A(x^2)+6) where f(u,v)=(u+v)^3+uv(27+9(u+v)-uv) - Michael Somos Jun 16 2004
Expansion of eta(q^3)^12/(eta(q)eta(q^9))^6-6 in powers of q.
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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).
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).
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
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Index entries for McKay-Thompson series for Monster simple group
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EXAMPLE
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T9A = 1/q + 27*q + 86*q^2 + 243*q^3 + 594*q^4 + 1370*q^5 + 2916*q^6 + ...
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PROGRAM
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(PARI) a(n)=local(A); if(n<-1, 0, n++; A=x*O(x^n); polcoeff(eta(x^3+A)^12/(eta(x+A)*eta(x^9+A))^6-6*x, n)) /* Michael Somos Jun 16 2004 */
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CROSSREFS
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Cf. A045491.
Sequence in context: A035074 A036925 A028993 this_sequence A098320 A034990 A090949
Adjacent sequences: A007263 A007264 A007265 this_sequence A007267 A007268 A007269
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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