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Search: id:A111374
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| A111374 |
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Series expansion of the Goellnitz-Gordon continued fraction 1 + q + q^2/(1 + q^3 + q^4/(1 + q^5 + q^6/(1 + q^7+ ...))). |
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4
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| 1, 1, 1, 0, 0, -1, -1, 0, 1, 2, 1, 0, -2, -3, -2, 0, 3, 4, 4, 0, -4, -6, -5, 0, 5, 9, 6, 0, -8, -12, -9, 0, 12, 16, 13, 0, -14, -22, -17, 0, 18, 29, 21, 0, -26, -38, -28, 0, 34, 50, 39, 0, -42, -64, -49, 0, 53, 82, 60, 0, -70, -105, -78, 0, 90, 132, 101, 0, -110, -166, -125, 0, 137, 208, 153, 0, -174, -258, -192, 0, 217
(list; graph; listen)
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OFFSET
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0,10
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REFERENCES
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S.-D. Chen and S.-S. Huang, On the series expansion of the Goellnitz-Gordon continued fraction, Internat. J. Number Theory, 1 (2005), 53-63.
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FORMULA
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Let qf(a, q) = Product(1-a*q^j, j=0..infinity); g.f. is qf(q^3, q^8)*qf(q^5, q^8)/(qf(q, q^8)*qf(q^7, q^8)).
Expansion of (phi(q)+phi(q^2))/(2*psi(q^4)) = 2*q*psi(q^4)/(phi(q)-phi(q^2)) in powers of q where phi(),psi() are Ramanujan theta functions. - Michael Somos Feb 15 2006
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EXAMPLE
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1/q +q +q^3 -q^9 -q^11 +q^15 +2*q^17 +q^19 -2*q^23 +...
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MAPLE
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M:=100; qf:=(a, q)->mul(1-a*q^j, j=0..M); t2:=qf(q^3, q^8)*qf(q^5, q^8)/(qf(q, q^8)*qf(q^7, q^8)); series(%, q, M); seriestolist(%);
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CROSSREFS
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Cf. A003823. G.f. is reciprocal of that of A092869.
Sequence in context: A157225 A055347 A055288 this_sequence A072739 A030399 A128763
Adjacent sequences: A111371 A111372 A111373 this_sequence A111375 A111376 A111377
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 09 2005
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