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Search: id:A113297
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| A113297 |
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Expansion of q^(-1/4) * eta(q) * eta(q^14) / ( eta(q^2) * eta(q^7) ) in powers of q. |
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1
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| 1, -1, 0, -1, 1, -1, 1, 0, 1, -2, 1, -1, 2, -2, 3, -3, 3, -4, 4, -4, 5, -4, 4, -6, 6, -7, 7, -8, 11, -11, 10, -12, 14, -15, 15, -14, 17, -20, 19, -21, 24, -26, 30, -31, 32, -37, 38, -40, 45, -44, 47, -54, 56, -60, 64, -68, 79, -83, 83, -92, 100, -105, 110, -112, 123, -136, 138, -147, 160, -170, 185, -194, 203
(list; graph; listen)
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OFFSET
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0,10
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LINKS
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F. G. Garvan and H. Yesilyurt, Shifted and shiftless partition identities II
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FORMULA
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Euler transform of period 14 sequence [ -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 0, ...].
G.f. A(x) = G(x^7)H(x^2)-x*G(x^2)H(x^7) where G(x)=g.f. A003114 and H(x)=g.f. A003106 are the Rogers-Ramanujan functions.
G.f.: Product_{k>0} (1+x^(7k))/(1+x^k) = 1/A097793(x).
Expansion of chi(-q) / chi(-q^7) in powers of q where chi() is a Ramanujan theta function.
G.f. is a period 1 Fourier series of a level 224 modular function which satisfies f(-1 / (224 t)) = f(t) where q = exp(2 pi i t).
G.f. is product k>0 P14(x^k) where P14 is 14th cyclotomic polynomial.
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EXAMPLE
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1/T56B = q -q^5 -q^13 +q^17 -q^21 +q^25 +q^33 -2*q^37 +q^41 -...
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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+A)*eta(x^14+A)/eta(x^2+A)/eta(x^7+A), n))}
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CROSSREFS
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Convolution inverse of A097793.
Adjacent sequences: A113294 A113295 A113296 this_sequence A113298 A113299 A113300
Sequence in context: A029333 A029261 A100480 this_sequence A119985 A116560 A103784
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Oct 23 2005
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