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A003295
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McKay-Thompson series of class 11A for the Monster group with a(0) = -5.
(Formerly M3872)
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3
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1, -5, 17, 46, 116, 252, 533, 1034, 1961, 3540, 6253, 10654, 17897, 29284, 47265, 74868, 117158, 180608, 275562, 415300, 620210, 916860, 1344251, 1953974, 2819664, 4038300, 5746031, 8122072, 11413112, 15943576, 22153909, 30620666
(list;
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listen;
history;
text;
internal format)
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OFFSET
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-1,2
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COMMENTS
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Coefficients of a modular function denoted by B(tau) in Atkin (1967).
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REFERENCES
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A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J., 8 (1967), 14-32.
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
N. D. Elkies, Elliptic and modular curves over finite fields and related computational issues, in AMS/IP Studies in Advanced Math., 7 (1998), 21-76; see p. 42.
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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=-1..30.
Index entries for McKay-Thompson series for Monster simple group
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FORMULA
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Contribution of Michael Somos, Aug 31 2012: (Start)
Expansion of -11 + (1 + 3*F)^2 * (1/F + 1 + 3*F) where F = eta(q^3) * eta(q^33) / (eta(q) * eta(q^11)) (= g.f. of A128663) in powers of q.
G.f. is Fourier series of a level 11 modular function. f(-1 / (11 t)) = f(t) where q = exp(2 pi i t).
A000521(n) = a(n) + 11 * a(11*n) unless n=0. [Atkin (1967) p. 22]
a(n) = A003295(n) = A058205(n) = A128525(n) = A134784(n) unless n=0. (End)
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EXAMPLE
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1/q - 5 + 17*q + 46*q^2 + 116*q^3 + 252*q^4 + 533*q^5 + 1034*q^6 + ...
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Cf. A003295, A058205, A128525, A128663, A134784.
Sequence in context: A146264 A146216 A046787 * A011853 A215053 A213767
Adjacent sequences: A003292 A003293 A003294 * A003296 A003297 A003298
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KEYWORD
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sign,nice,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 05 2000
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STATUS
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approved
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