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Search: id:A030181
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| A030181 |
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Expansion of (eta(q)/ eta(q^7))^4 in powers of q. |
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+0
2
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| 1, -4, 2, 8, -5, -4, -10, 12, -7, 8, 46, -36, -26, -44, 46, -28, 42, 188, -132, -96, -167, 172, -98, 120, 596, -420, -286, -492, 496, -280, 368, 1680, -1151, -792, -1332, 1320, -735, 916, 4264, -2908, -1960, -3252, 3200, -1764, 2230, 10104, -6798, -4560, -7536
(list; graph; listen)
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OFFSET
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-1,2
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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.
N. D. Elkies, Elliptic and modular curves..., in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 66.
N. Elkies, The Klein quartic in number theory, pp. 51-101 of S. Levy, ed., The Eightfold Way, Cambridge Univ. Press, 1999. MR1722413 (2001a:11103)
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
N. Elkies, The Klein quartic in number theory
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FORMULA
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Euler transform of period 7 sequence [ -4, -4, -4, -4, -4, -4, 0, ...] . - Michael Somos Mar 15 2004
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= (u-v)^2* (u+v) -u*v* (u+7)*(v+7) . - Michael Somos Feb 19 2007
(Apart from constant term) McKay-Thompson series of class 7B for Monster (cf. A052240).
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PROGRAM
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(PARI) {a(n)= local(A); if(n<-1, 0, n++; A=x*O(x^n); polcoeff( (eta(x+A)/ eta(x^7+A))^4, n))} /* Michael Somos Feb 19 2007 */
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CROSSREFS
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Essentially same as A052240.
Sequence in context: A141073 A131819 A000727 this_sequence A021879 A020806 A030210
Adjacent sequences: A030178 A030179 A030180 this_sequence A030182 A030183 A030184
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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