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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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1
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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; refs; listen; history; internal format)
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OFFSET
| -1,2
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COMMENTS
| McKay-Thompson series of class 7B for the Monster group with a(0) = -4.
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REFERENCES
| 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)
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
| N. Elkies, The Klein quartic in number theory
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
Index entries for McKay-Thompson series for Monster simple group
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FORMULA
| 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
a(n) = A052240(n) unless n = 0.
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EXAMPLE
| 1/q - 4 + 2*q + 8*q^2 - 5*q^3 - 4*q^4 - 10*q^5 + 12*q^6 - 7*q^7 + 8*q^8 + ...
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PROG
| (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
| Cf. A052240.
Sequence in context: A191536 A187076 A000727 * A021879 A020806 A030210
Adjacent sequences: A030178 A030179 A030180 * A030182 A030183 A030184
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KEYWORD
| sign,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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