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Search: id:A007248
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| A007248 |
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McKay-Thompson series of class 4C for the Monster group.
(Formerly M5084)
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+0
7
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| 1, 20, -62, 216, -641, 1636, -3778, 8248, -17277, 34664, -66878, 125312, -229252, 409676, -716420, 1230328, -2079227, 3460416, -5677816, 9198424, -14729608, 23328520, -36567242, 56774712, -87369461, 133321908, -201825396, 303248408, -452431503
(list; graph; listen)
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OFFSET
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0,2
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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 A. Sebbar, Fuchsian groups, automorphic functions and Schwarzians, Math. Ann., 318 (2000), 255-275.
McKay, John; Strauss, Hubertus. 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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FORMULA
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16*(theta_3/theta_2)^4 - 8 = 16/lambda(z) - 8.
Expansion of q*(-8 +16/lambda(z)) in powers of q^2 where nome q = exp(pi*i*z). - Michael Somos Nov 14 2006
Expansion of q*(8 + (eta(q)/eta(q^4))^8) in powers of q^2. - Michael Somos Nov 14 2006
Given g.f. A(x), then B(x)=A(x^2)/x satisfies 0=f(B(x), B(x^2)) where f(u, v) = (v+24)^2 -(v+8)*u^2 . - Michael Somos Nov 14 2006
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EXAMPLE
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T4C = 1/q + 20*q - 62*q^3 + 216*q^5 - 641*q^7 + 1636*q^9 - 3778*q^11 + ...
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PROGRAM
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(PARI) 8*x+prod(n=1, 39, if(n%4, 1-x^n, 1), 1+O(x^40))^8
(PARI) {a(n)=local(A); if(n<0, 0, n*=2; A=x*O(x^n); polcoeff( 8*x+(eta(x+A)/eta(x^4+A))^8, n))} /* Michael Somos Nov 14 2006 */
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CROSSREFS
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A029845(2n-1) = A124972(2n-1) = a(n). - Michael Somos Nov 14 2006.
Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Sequence in context: A041784 A105092 A112144 this_sequence A117431 A117432 A033577
Adjacent sequences: A007245 A007246 A007247 this_sequence A007249 A007250 A007251
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KEYWORD
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sign,easy
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AUTHOR
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njas
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