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Search: id:A132319
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| A132319 |
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Expansion of q^-1 * (chi(-q) * chi(-q^7))^3 in powers of q where chi() is a Ramanujan theta function. |
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1
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| 1, -3, 3, -4, 9, -12, 15, -24, 39, -52, 66, -96, 130, -168, 219, -292, 390, -492, 625, -804, 1023, -1280, 1599, -2016, 2508, -3096, 3807, -4688, 5760, -7020, 8532, -10368, 12585, -15156, 18213, -21912, 26287, -31404, 37410, -44584, 53004, -62784, 74245, -87768, 103578
(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 (eta(q) * eta(q^7)/( eta(q^2) * eta(q^14)))^3 in powers of q.
Euler transform of period 14 sequence [ -3, 0, -3, 0, -3, 0, -6, 0, -3, 0, -3, 0, -3, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^2 * v - v^2 + 8 * u + 6 * u * v.
G.f. is a Fourier series which satisfies f(-1 / (14 t)) = 8 / f(t) where q = exp(2 pi i t).
G.f.: x^-1 * (Product_{k>0} (1+x^k) * (1+x^(7*k)))^-3.
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EXAMPLE
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1/q - 3 + 3*q - 4*q^2 + 9*q^3 - 12*q^4 + 15*q^5 - 24*q^6 + 39*q^7 - ...
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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^7+A) / eta(x^2+A) / eta(x^14+A))^3, n))}
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CROSSREFS
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A058503(n) = a(n) unless n = 0.
Sequence in context: A065678 A022598 A107635 this_sequence A130626 A115284 A144626
Adjacent sequences: A132316 A132317 A132318 this_sequence A132320 A132321 A132322
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 18 2007
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