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Search: id:A007259
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| A007259 |
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Expansion of Product (1+q^m)^(-8); m=1..inf.
(Formerly M4504)
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+0
2
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| 1, -8, 28, -64, 134, -288, 568, -1024, 1809, -3152, 5316, -8704, 13990, -22208, 34696, -53248, 80724, -121240, 180068, -264448, 384940, -556064, 796760, -1132544, 1598789, -2243056, 3127360, -4333568, 5971922, -8188096, 11170160, -15163392, 20491033, -27572936
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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McKay-Thompson series of class 6F for the Monster group.
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REFERENCES
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T. J. I'a. Bromwich, Introduction to the Theory of Infinite Series, Macmillan, 2nd. ed. 1949, p. 118, Problem 24.
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 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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FORMULA
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Expansion of chi(-q)^8 in powers of q where chi() is a Ramanujan theta function. - Michael Somos Aug 18 2007
Expansion of q^(-1/3) * (eta(q) / eta(q^2))^8 in powers of q. - Michael Somos Aug 18 2007
Euler transform of period 2 sequence [ -8, 0, ...]. - Michael Somos Aug 18 2007
Given g.f. A(x), then B(x) = A(x^3)/x satisfies 0 = f(B(x), B(x^2)) where f(u, v) = v^2 - u^2 * v - 16 * u. - Michael Somos Aug 18 2007
G.f. is a Fourier series which satisfies f(-1/(2 t)) = 16/ f(t) where q = exp(2 pi i t). - Michael Somos Aug 18 2007
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EXAMPLE
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T6F = 1/q - 8q^2 + 28q^5 - 64q^8 + 134q^11 - 288q^14 + 568q^17 + ...
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x+A)/eta(x^2+A))^8, n))}
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CROSSREFS
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Sequence in context: A033580 A002408 A007331 this_sequence A101127 A134747 A083013
Adjacent sequences: A007256 A007257 A007258 this_sequence A007260 A007261 A007262
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KEYWORD
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sign,easy,nice
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AUTHOR
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njas
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