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Search: id:A123676
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| A123676 |
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Expansion of b(q)*c(q^3)/(b(q^2)*c(q^6)) in powers of q where b(),c() are cubic AGM analog functions. |
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1
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| 1, -3, 3, -2, 3, -6, 10, -12, 15, -22, 30, -36, 44, -60, 78, -96, 117, -150, 190, -228, 276, -340, 420, -504, 603, -732, 885, -1052, 1245, -1488, 1770, -2088, 2454, -2902, 3420, -3996, 4666, -5460, 6378, -7400, 8583, -9972, 11566, -13344, 15378, -17752, 20448, -23472, 26904, -30876
(list; graph; listen)
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OFFSET
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-1,2
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FORMULA
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Expansion of q^(-1)*(chi(-q)*chi(-q^9))^3/chi(-q^3)^2 in powers of q where chi() is a Ramanjuan theta function.
Euler transform of period 18 sequence [ -3, 0, -1, 0, -3, 0, -3, 0, -4, 0, -3, 0, -3, 0, -1, 0, -3, 0, ...].
Given g.f. A(x), then B(x)=1/A(x) satisfies 0=f(B(x), B(x^2)) where f(u,v)= u^2 -v -u*(6*v +4*v^2).
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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^9+A)/eta(x^2+A)/eta(x^18+A))^3* (eta(x^6+A)/eta(x^3+A))^2, n))}
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CROSSREFS
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Convolution inverse of A123629.
Cf. A058533. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 13 2008]
Sequence in context: A057853 A129309 A003560 this_sequence A122775 A086632 A038699
Adjacent sequences: A123673 A123674 A123675 this_sequence A123677 A123678 A123679
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Oct 05 2006
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