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Search: id:A109063
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| A109063 |
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Expansion of eta(q)/eta(q^5)^5 in powers of q. |
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+0
1
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| 1, -1, -1, 0, 0, 6, -5, -4, 0, 0, 25, -20, -16, 0, 0, 84, -65, -50, 0, 0, 250, -190, -144, 0, 0, 676, -505, -376, 0, 0, 1706, -1260, -929, 0, 0, 4064, -2970, -2166, 0, 0, 9243, -6700, -4850, 0, 0, 20200, -14535, -10444, 0, 0, 42677, -30520, -21802, 0, 0, 87512, -62235, -44212, 0, 0, 174814
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OFFSET
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-1,6
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REFERENCES
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W. Duke, Continued fractions and modular functions, Bull. Amer. Math. Soc. 42 (2005), 137-162. See page 150.
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FORMULA
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Euler transform of period 5 sequence [ -1, -1, -1, -1, 4, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=u^2*w^2 +2*u*v^2*w +4*u*v^3 -v^3*w.
G.f.: (1/x)Product_{k>0} (1-x^k)/(1-x^(5k))^5 . a(5n+2)=a(5n+3)=0.
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EXAMPLE
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1/q -1 -q + 6*q^4 -5*q^5 -4*q^6 + 25*q^9 -20*q^10 -16*q^11 +...
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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^5+A)^5, n))}
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CROSSREFS
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Sequence in context: A021609 A019686 A021157 this_sequence A110390 A084448 A085664
Adjacent sequences: A109060 A109061 A109062 this_sequence A109064 A109065 A109066
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jun 17 2005
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