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Search: id:A132966
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| A132966 |
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Expansion of f(-q) * chi(q^2)^2 in powers of q where f(), chi() are Ramanujan theta functions. |
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2
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| 1, -1, 1, -2, -1, 0, 1, 1, 2, -1, 0, -1, 0, 1, -1, 1, 2, -2, 1, -2, -3, 0, 0, 1, 2, 0, 1, -2, -2, 2, 0, 2, 3, -3, 1, -3, -3, 2, 0, 4, 4, -2, 0, -3, -3, 2, -2, 3, 5, -3, 1, -6, -6, 2, 0, 5, 6, -3, 1, -4, -6, 4, -2, 6, 7, -5, 3, -8, -9, 5, -1, 7, 9, -5, 2, -8, -9, 7, -2, 9, 12, -7, 3, -10, -13, 6, -2, 11, 13, -7, 1, -11, -14, 8, -4, 13, 17, -11, 5, -17
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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Expansion of q^(1/8) * eta(q^4)^4 * eta(q) / (eta(q^2)^2 * eta(q^8)^2) in powers of q.
Euler transform of period 8 sequence [ -1, 1, -1, -3, -1, 1, -1, -1, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (256 t)) = 32^(1/2) (t/i)^(1/2) g(t) where q = exp(2 pi i t) and g() is g.f. for A132965.
G.f.: Product_{k>0} (1 - x^k) * (1 + x^(2*k))^2 / (1 + x^(4*k))^2.
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EXAMPLE
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q^-1 - q^7 + q^15 - 2*q^23 - q^31 + q^47 + q^55 + 2*q^63 - q^71 - ...
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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^4 + A)^4 * eta(x + A) / eta(x^2 + A)^2 / eta(x^8 + A)^2, n))}
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CROSSREFS
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Sequence in context: A132004 A143110 A109294 this_sequence A037897 A054070 A126304
Adjacent sequences: A132963 A132964 A132965 this_sequence A132967 A132968 A132969
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 23 2007
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