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Search: id:A132301
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| A132301 |
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Expansion of q^(1/3) * eta(q)^3/( eta(q^2) * eta(q^3) * eta(q^6) ) in powers of q. |
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2
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| 1, -3, 1, 3, -1, 0, 1, -6, 0, 6, -3, 3, 4, -12, 1, 12, -6, 3, 5, -24, 1, 24, -10, 6, 11, -42, 4, 42, -19, 12, 17, -72, 4, 69, -31, 18, 31, -120, 9, 114, -50, 30, 46, -189, 11, 180, -79, 48, 77, -294, 21, 276, -122, 72, 112, -450, 28, 420, -183, 108, 173, -672, 46, 624, -273, 162, 249, -987, 62, 912
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Euler transform of period 6 sequence [ -3, -2, -2, -2, -3, 0, ...].
Given g.f. A(x), then B(x) = A(x^3)/(3*x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (v^2 - 2*u)^3 -u^4 * (2*u - 3*v^2) * (4*u - 3*v^2).
G.f. is a period 1 Fourier series which satisfies f(-1/ (36 t)) = 6 g(t) where q = exp(2 pi i t) and g() is g.f. for A132302.
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EXAMPLE
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1/q - 3*q^2 + q^5 + 3*q^8 - q^11 + q^17 - 6*q^20 + 6*q^26 - 3*q^29 + ...
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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)^3/ eta(x^2+A)/ eta(x^3+A)/ eta(x^6+A), n))}
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CROSSREFS
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Sequence in context: A144477 A079530 A020815 this_sequence A073272 A121273 A063065
Adjacent sequences: A132298 A132299 A132300 this_sequence A132302 A132303 A132304
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 17 2007
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