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Search: id:A132968
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| A132968 |
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Expansion of chi(-q) * chi(-q^15) / ( chi(-q^6) * chi(-q^10) ) in powers of q where chi() is a Ramanaujan theta function. |
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+0
2
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| 1, -1, 0, -1, 1, -1, 2, -2, 2, -3, 4, -4, 5, -6, 6, -9, 11, -10, 14, -16, 17, -22, 24, -26, 32, -37, 40, -47, 54, -58, 70, -80, 84, -100, 112, -122, 143, -158, 172, -198, 222, -242, 274, -306, 332, -379, 422, -454, 515, -569, 620, -698, 766, -834, 932, -1028, 1118, -1240, 1364, -1480, 1645, -1806, 1952
(list; graph; listen)
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OFFSET
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0,7
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FORMULA
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Expansion of eta(q) * eta(q^12) * eta(q^15) * eta(q^20) / ( eta(q^2) * eta(q^6) * eta(q^10) * eta(q^30) ) in powers of q.
Euler transform of period 60 sequence [ -1, 0, -1, 0, -1, 1, -1, 0, -1, 1, -1, 0, -1, 0, -2, 0, -1, 1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 2, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 1, -1, 0, -2, 0, -1, 0, -1, 1, -1, 0, -1, 1, -1, 0, -1, 0, -1, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = 1 - f(t) where q = exp(2 pi i t).
G.f.: Product_{k>0} (1 + x^(6*k)) * (1 + x^(10*k)) / ( (1 + x^k) * (1 + x^(15*k)) ).
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EXAMPLE
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1 - q - q^3 + q^4 - q^5 + 2*q^6 - 2*q^7 + 2*q^8 - 3*q^9 + 4*q^10 - ...
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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^12 + A) * eta(x^15 + A) * eta(x^20 + A) / eta(x^2 + A) / eta(x^6 + A) / eta(x^10 + A) / eta(x^30 + A), n))}
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CROSSREFS
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A132967(n) = -a(n) unless n=0.
Sequence in context: A067357 A051059 A132967 this_sequence A029075 A029052 A131795
Adjacent sequences: A132965 A132966 A132967 this_sequence A132969 A132970 A132971
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Sep 02 2007
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