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A058601
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McKay-Thompson series of class 27b for the Monster group.
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2
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1, 2, 5, 6, 12, 16, 27, 34, 51, 70, 101, 134, 182, 240, 322, 416, 544, 696, 902, 1144, 1462, 1832, 2317, 2882, 3608, 4454, 5524, 6786, 8352, 10200, 12463, 15136, 18384, 22210, 26826, 32250, 38768, 46408, 55531, 66186, 78859, 93638, 111123, 131462, 155428, 183280
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| 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
| Index entries for McKay-Thompson series for Monster simple group
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FORMULA
| Expansion of q^(1/3) * eta(q^3)^4 / (eta(q) * eta(q^9))^2 in powers of q. - Michael Somos Jun 30 2011
Expansion of q^(1/3) * ( (c(q) * b(q^3)) / (b(q) * c(q^3)) )^(1/2) in powers of q where b(), c() are cubic AGM functions. - Michael Somos Jun 30 2011
Euler transform of period 9 sequence [ 2, 2, -2, 2, 2, -2, 2, 2, 0, ...]. - Michael Somos Jun 30 2011
Given g.f. A(x) then B(x) = A(x^3) / x satisifes 0 = f(B(x), B(x^2)) where f(u, v) = (u^2 - v) * (u - v^2) + 4*u*v. - Michael Somos Jun 30 2011
G.f. is a period 1 Fourier series which satisfies f(-1 / (81 t)) = f(t) where q = exp(2 pi i t). - Michael Somos Jun 30 2011
G.f.: Product_{k>0} (1 - x^(3*k))^4 / ((1 - x^k) * (1 - x^(9*k)))^2.
a(n) = A058096(3*n).
Convolution inverse of A192329.
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EXAMPLE
| T27b = 1/q + 2*q^2 + 5*q^5 + 6*q^8 + 12*q^11 + 16*q^14 + 27*q^17 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A)^4 / (eta(x + A) * eta(x^9 + A))^2, n))} /* Michael Somos Jun 30 2011 */
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CROSSREFS
| Cf. A000521, A007240, A014708, A007241, A007267, A045478, A192329.
Sequence in context: A153485 A023143 A085206 * A108365 A064765 A082552
Adjacent sequences: A058598 A058599 A058600 * A058602 A058603 A058604
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 27, 2000
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