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Search: id:A132321
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| A132321 |
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Expansion of q^-1 * chi(-q) * chi(-q^3) * chi(-q^5) * chi(-q^15) in powers of q where chi() is a Ramanujan theta function. |
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+0
1
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| 1, -1, 0, -2, 2, -2, 3, -2, 5, -6, 5, -6, 9, -10, 10, -16, 17, -18, 25, -26, 31, -38, 37, -48, 60, -62, 68, -84, 95, -104, 125, -134, 154, -182, 192, -220, 257, -274, 309, -360, 394, -434, 492, -544, 607, -688, 740, -824, 944, -1018, 1123, -1266, 1377, -1524, 1697, -1850, 2041, -2264, 2461, -2708
(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) * eta(q^3) * eta(q^5) * eta(q^15) / (eta(q^2) * eta(q^6) * eta(q^10) * eta(q^30)) in powers of q.
Euler transform of period 30 sequence [ -1, 0, -2, 0, -2, 0, -1, 0, -2, 0, -1, 0, -1, 0, -4, 0, -1, 0, -1, 0, -2, 0, -1, 0, -2, 0, -2, 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. is a Fourier series which satisfies f(-1 / (30 t)) = 4 / f(t) where q = exp(2 pi i t).
G.f.: x^-1 * (Product_{k>0} (1+x^k) * (1+x^(3*k)) * (1+x^(5*k)) * (1+x^(15*k)))^-1.
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EXAMPLE
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q^-1 - 1 - 2*q^2 + 2*q^3 - 2*q^4 + 3*q^5 - 2*q^6 + 5*q^7 - 6*q^8 + ...
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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^3+A) * eta(x^5+A) * eta(x^15+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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A058614(n) = a(n) unless n = 0.
Adjacent sequences: A132318 A132319 A132320 this_sequence A132322 A132323 A132324
Sequence in context: A104239 A058614 A058726 this_sequence A122765 A131053 A125600
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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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