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A058511
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McKay-Thompson series of class 15D for the Monster group.
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0
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1, -2, -1, 2, 1, 4, -6, -2, 2, 0, 10, -14, -5, 8, 4, 20, -28, -10, 14, 4, 39, -56, -20, 28, 10, 72, -100, -34, 46, 16, 128, -176, -61, 86, 30, 216, -294, -100, 134, 44, 355, -484, -165, 226, 79, 568, -770, -260, 350, 116, 894, -1208, -408, 552, 188, 1376, -1848, -620, 830, 276, 2087, -2800, -940
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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).
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
| Index entries for McKay-Thompson series for Monster simple group
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FORMULA
| Expansion of q^(1/3) * (eta(q) / eta(q^5))^2 in powers of q.
Euler transform of period 5 sequence [ -2, -2, -2, -2, 0, ...].
G.f. is a Fourier series which satisfies f(-1 / (45 t)) = 5 / f(t) where q = exp(2 pi i t).
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (u - v^2) * (v - u^2) + 4*u*v.
G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^4)) where f(u, v, w) = u^2 + u*w + w^2 - v^2 * (u + w) - 5*v.
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EXAMPLE
| T15D = 1/q - 2*q^2 - q^5 + 2*q^8 + q^11 + 4*q^14 - 6*q^17 - 2*q^20 + 2*q^23 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A) / eta(x^5 + A))^2, n))} /* Michael Somos Dec 17 2010 */
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CROSSREFS
| Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Sequence in context: A166235 A143591 A085063 * A106380 A076198 A032021
Adjacent sequences: A058508 A058509 A058510 * A058512 A058513 A058514
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 27, 2000
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