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A007266
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McKay-Thompson series of class 9A for Monster.
(Formerly M5192)
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2
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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
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OFFSET
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-1,3
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COMMENTS
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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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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.
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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Table of n, a(n) for n=-1..28.
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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PROG
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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 * A098320 A034990 A090949
Adjacent sequences: A007263 A007264 A007265 * 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.
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STATUS
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approved
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