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Search: id:A132980
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| A132980 |
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Expansion of q^(-1) * chi(-q^5)^5 / chi(-q) in powers of q. |
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2
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| 1, 1, 1, 2, 2, -2, -1, 0, -4, -2, 5, 2, 0, 8, 2, -8, -3, -2, -14, -6, 14, 6, 4, 24, 12, -24, -11, -4, -40, -16, 38, 16, 5, 62, 24, -60, -24, -10, -94, -40, 91, 38, 18, 144, 62, -136, -57, -24, -214, -88, 201, 82, 30, 308, 122, -288, -117, -48, -440, -180, 410, 168, 74, 624, 262, -578, -238, -96, -874, -356, 804
(list; graph; listen)
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OFFSET
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-1,4
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FORMULA
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Expansion of ( eta(q^5) / eta(q^10) )^5 / ( eta(q) / eta(q^2) ) in powers of q.
Euler transform of period 10 sequence [ 1, 0, 1, 0, -4, 0, 1, 0, 1, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^2 * v - v^2- 4 * u - 2 * u * v.
G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u - v)^4 - u * v * (u^2 - 3 * u - 4) * (v^2 - 3 * v - 4).
G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = 4 g(t) where q = exp(2 pi i t) and g() is g.f. for A132985.
G.f.: (1/x) * Product_{k>0} (1 + x^k) / (1 + x^(5*k))^5.
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EXAMPLE
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1/q + 1 + q + 2*q^2 + 2*q^3 - 2*q^4 - q^5 - 4*q^7 - 2*q^8 + 5*q^9 + ...
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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^2 + A) / eta(x + A) * ( eta(x^5 + A) / eta(x^10 + A) )^5, n))}
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CROSSREFS
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A058101(n) = a(n) unless n=0.
Sequence in context: A114898 A058101 A112159 this_sequence A106823 A029446 A029442
Adjacent sequences: A132977 A132978 A132979 this_sequence A132981 A132982 A132983
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Sep 07 2007
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