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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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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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LINKS
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Index entries for McKay-Thompson series for Monster simple group
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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 A159504 A117432
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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N. J. A. Sloane (njas(AT)research.att.com).
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