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Search: id:A117410
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| A117410 |
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Expansion of q^(-5/24) eta(q^2)^3/eta(q) in powers of q. |
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1
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| 1, 1, -1, 0, -1, -2, 1, -1, -1, 0, 1, 1, -1, 1, 0, 2, 1, 0, 0, -1, 2, 1, 0, -1, 0, -1, 0, -1, 1, 1, -3, 0, -1, -1, -1, 1, 0, 0, 0, -1, -2, 0, 1, 0, 1, 0, 1, 0, 0, -1, 2, -1, 0, 1, 1, 3, 0, -1, 0, 1, -1, 0, 1, 0, 0, 2, 0, 1, -1, 0, -2, -1, 1, 0, 0, -1, 0, 0, 1, -1, 0, -1, -1, -1, 0, -2, -1, 0, 2, 1, -2, 0, 1, -1, 0, -2, -1, 1, -1, 1, 0, 0, 0, 1, 0
(list; graph; listen)
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OFFSET
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0,6
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REFERENCES
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B. Gordon and D. Sinor, Multiplicative properties of eta-products, Number theory, Madras 1987, pp. 173-200, Lecture Notes in Math., 1395, Springer, Berlin, 1989. see page 183. MR1019331 (90k:11050)
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FORMULA
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Euler transform of period 2 sequence [ 1, -2, ...].
Given A=A0+A1+A2+Ae is the 5-section, then 0=A3*A1^2-A2*A4^2.
Given A=A0+A1+A2+A3+A4+A5+A6 is the 7-section, then 0=A0*A6+A1*A5+A2*A4+4*A3^2, A3=x^10*A(x^49).
G.f. Product_{k>0} (1+x^k)(1-x^(2k))^2.
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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^2+A)^3/eta(x+A), n))}
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CROSSREFS
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Cf. A107034(n)=(-1)^n*a(n).
Adjacent sequences: A117407 A117408 A117409 this_sequence A117411 A117412 A117413
Sequence in context: A117195 A156606 A107034 this_sequence A087810 A052314 A093718
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Mar 13 2006
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