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Search: id:A145708
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| A145708 |
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Expansion of psi(-q) / psi(-q^5) in powers of q where psi() is a Ramanujan theta function. |
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4
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| 1, -1, 0, -1, 0, 1, 0, 0, -1, 0, 2, 0, 0, -1, 0, 2, -1, 0, -2, 0, 3, -2, 0, -3, 0, 5, -2, 0, -3, 0, 6, -2, 0, -4, 0, 8, -3, 0, -6, 0, 11, -5, 0, -8, 0, 14, -6, 0, -10, 0, 18, -6, 0, -12, 0, 22, -9, 0, -16, 0, 28, -13, 0, -21, 0, 36, -14, 0, -25, 0, 44, -16, 0, -30, 0, 54, -22, 0, -38, 0, 67, -28, 0, -48, 0, 83, -32, 0, -57, 0, 100, -38
(list; graph; listen)
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OFFSET
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0,11
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FORMULA
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Expansion of q^(1/2) * eta(q) * eta(q^4) * eta(q^10) / (eta(q^2) * eta(q^5) * eta(q^20)) in powers of q.
Euler transform of period 20 sequence [ -1, 0, -1, -1, 0, 0, -1, -1, -1, 0, -1, -1, -1, 0, 0, -1, -1, 0, -1, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (80 t)) = 5^(1/2) / f(t) where q = exp(2 pi i t).
a(5*n + 2) = a(5*n + 4) = 0.
G.f.: (Product_{k>0} P(5, x^k) * P(20, x^k))^(-1) where P(n,x) is the nth cyclotomic polynomial.
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EXAMPLE
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1/q - q - q^5 + q^9 - q^15 + 2*q^19 - q^25 + 2*q^29 - q^31 - 2*q^35 + ...
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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^4 + A) * eta(x^10 + A) / (eta(x^2 + A) * eta(x^5 + A) * eta(x^20 + A)), n))}
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CROSSREFS
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Convolution square is A145740. Convolution inverse is A036026. (-1)^n * A138532(n) = a(n). - A036026(n) = a(5*n + 3).
Sequence in context: A084143 A025888 A138532 this_sequence A065293 A164615 A054876
Adjacent sequences: A145705 A145706 A145707 this_sequence A145709 A145710 A145711
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Oct 17 2008
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