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A107033
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Expansion of q^(-1/24) eta(q^2)^8/(eta(q)^3 eta(q^4)^3) in powers of q.
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1
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1, 3, 1, -2, 2, 1, -4, -1, -2, 0, 2, -4, -1, -2, -2, 1, 0, 2, -2, 2, 0, -4, 1, 0, 2, 2, 5, 0, -2, 0, 0, 4, -2, 0, 0, 3, 4, 0, 0, 2, 1, -4, 2, -2, 0, 0, 0, 2, -2, 0, 2, 3, -2, 0, -2, -2, -4, -1, 0, 0, 0, -4, 2, 0, 4, 0, -4, -2, 0, -2, -1, 0, 0, -2, -2, 2, -6, 1, 2, 0, 0, 4, 0, -2, 2, 0, 0, -2, -2, -2, 2, 0, 1, 0, 0, -2, 4, 0, 0, 2, 1, 6, 0, 2, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339, see page 333.
H. Kahl, G. Koehler, Components of Hecke theta series, J. Math. Anal. Appl. 232 (1999), no. 2, 312-331, see page 320. MR1683136 (2000e:11051)
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FORMULA
| Euler transform of period 4 sequence [3, -5, 3, -2, ...].
G.f. Product_{k>0} (1-x^(2k))^2(1+x^k)^3/(1+x^(2k))^3.
Expansion of f(sqrt(-x)) * f(-sqrt(-x)) in powers of x where f() is a Ramanujan theta function. - Michael Somos Aug 23 2010
Expansion of f(x) * phi(x) in powers of x where f() and phi() are Ramanujan theta functions. - Michael Somos Aug 23 2010
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EXAMPLE
| 1 + 3*x + x^2 - 2*x^3 + 2*x^4 + x^5 - 4*x^6 - x^7 - 2*x^8 + 2*x^10 + ...
Alternatively, q + 3*q^25 + q^49 - 2*q^73 + 2*q^97 + q^121 - 4*q^145 - q^169 - 2*q^193 + ...
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^8/eta(x+A)^3/eta(x^4+A)^3, n))}
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CROSSREFS
| Sequence in context: A088429 A111951 * A115110 A066635 A016568 A021888
Adjacent sequences: A107030 A107031 A107032 * A107034 A107035 A107036
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KEYWORD
| sign
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AUTHOR
| Michael Somos, May 09 2005
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