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Search: id:A132179
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| A132179 |
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Expansion of q^(1/6) * eta(q^2)^3 / ( eta(q) * eta(q^3) * eta(q^6)) in powers of q. |
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+0
5
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| 1, 1, -1, 1, 0, -3, 4, 1, -6, 5, 1, -10, 11, 4, -19, 17, 4, -31, 31, 9, -50, 46, 11, -79, 77, 21, -122, 112, 28, -183, 173, 46, -273, 249, 62, -396, 370, 98, -573, 521, 130, -815, 751, 193, -1149, 1041, 261, -1599, 1461, 373, -2214, 1998, 498, -3031, 2750, 696, -4125, 3708, 923, -5567
(list; graph; listen)
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OFFSET
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0,6
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FORMULA
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Euler transform of period 6 sequence [ 1, -2, 2, -2, 1, 0, ...].
Given g.f. A(x), then B(x) = A(x^6)/x satisfies 0 = f(B(x), B(x^2)) where f(u, v) = (u^2- 3*v)^3 - 4*(u^2*v^2 - v^3)*(u^2*v^2 -2*v^3).
G.f.: Product_{k>0} (1+x^k)^2/( (1-x^k+x^(2*k))* (1+x^k+x^(2*k))^2).
G.f. is a period 1 Fourier series which satisfies f(-1/ (36 t)) = (3/2) g(t) where q = exp(2 pi i t) and g() is g.f. for A132180.
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EXAMPLE
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1/q + q^5 - q^11 + q^17 - 3*q^29 + 4*q^35 + q^41 - 6*q^47 + 5*q^53 + ...
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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^2+A)^3/ eta(x+A)/ eta(x^3+A)/ eta(x^6+A), n))}
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CROSSREFS
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A062242(2*n) = a(n).
Sequence in context: A114156 A143771 A030707 this_sequence A089029 A131226 A132700
Adjacent sequences: A132176 A132177 A132178 this_sequence A132180 A132181 A132182
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 12 2007
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