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Search: id:A058543
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| A058543 |
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McKay-Thompson series of class 18e for the Monster group. |
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+0
1
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| 1, -2, 1, -4, 8, -6, 10, -16, 18, -26, 33, -40, 58, -74, 82, -112, 147, -166, 212, -268, 316, -392, 476, -560, 695, -838, 967, -1184, 1430, -1648, 1970, -2352, 2731, -3236, 3803, -4404, 5206, -6080, 6984, -8192, 9553, -10942, 12709, -14736, 16886, -19506, 22448, -25648, 29552
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
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LINKS
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Index entries for McKay-Thompson series for Monster simple group
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FORMULA
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Expansion of chi(-q)^2 * chi(-q^3)^2 in powers of q where chi() is a Ramanujan theta function. - Michael Somos Aug 18 2007
Expansion of q^(-1/3) * (eta(q) * eta(q^3) / (eta(q^2) * eta(q^6)))^2 in powers of q. - Michael Somos Aug 18 2007
Euler transform of period 6 sequence [ -2, 0, -4, 0, -2, 0, ...]. - Michael Somos Aug 18 2007
Given g.f. A(x), then B(x) = A(x^3)/x satisfies 0 = f(B(x), B(x^2)) where f(u, v) = v^2 - u^2 * v - 4 * u. - Michael Somos Aug 18 2007
G.f. is a Fourier series which satisfies f(-1/(6 t)) = 4/ f(t) where q = exp(2 pi i t). - Michael Somos Aug 18 2007
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EXAMPLE
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T18e = 1/q - 2*q^2 + q^5 - 4*q^8 + 8*q^11 - 6*q^14 + 10*q^17 - 16*q^20 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if(n<0, 0, A = x*O(x^n); polcoeff( (eta(x+A) * eta(x^3+A) / eta(x^2+A) / eta(x^6+A))^2, n))} /* Michael Somos Aug 18 2007 */
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Sequence in context: A158451 A118272 A112173 this_sequence A156817 A008301 A113820
Adjacent sequences: A058540 A058541 A058542 this_sequence A058544 A058545 A058546
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 27, 2000
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