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Search: id:A030197
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| A030197 |
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McKay-Thompson series of class 3A for Monster. Expansion of Hauptmodul for X_0^{+}(3). |
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+0
5
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| 1, 42, 783, 8672, 65367, 371520, 1741655, 7161696, 26567946, 90521472, 288078201, 864924480, 2469235686, 6748494912, 17746495281, 45086909440, 111066966315, 266057139456, 621284327856, 1417338712800, 3164665156308
(list; graph; listen)
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OFFSET
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-1,2
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COMMENT
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Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 21 2009: (Start)
(1 + 42x + 783x^2 + 8672x^3 + ...) = the convolution square of (1 + 21x +
171x^2 + 745x^3 + ...), where A007261 = (1, 21, 171, 745, 2418,...).) (End)
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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.
N. D. Elkies, Elliptic and modular curves..., in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 39.
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
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Index entries for McKay-Thompson series for Monster simple group
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FORMULA
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Expansion of (h+27)^2/h, where h = (eta(q)/eta(q^3))^12.
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EXAMPLE
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1/q + 42 + ...
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CROSSREFS
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Apart from constant term, same as A007243, A045480.
A007261 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 21 2009]
Sequence in context: A091962 A007746 A159947 this_sequence A020933 A030020 A090969
Adjacent sequences: A030194 A030195 A030196 this_sequence A030198 A030199 A030200
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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