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A188578
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Expansion of (1 - x^3) * (1 - x^5) * (1 - x^6) / (1 - x^15) in powers of x.
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0
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1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..104.
M. Somos, Rational Function Multiplicative Coefficients
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FORMULA
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Euler transform of length 15 sequence [ 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1].
a(n) = b(2*n + 1) where b(n) is multiplicative with b(p^e) = 0^e if p<7, b(p^e) = 1, if p == 1, 17, 19, 23 (mod 30), b(p^e) = (-1)^e if p == 7, 11, 13, 29 (mod 30).
G.f.: (1 - x^3) * (1 - x^5) * (1 - x^6) / (1 - x^15). a(-1 - n) = -a(n).
G.f. (1-x)^2 *(1+x) *(1+x+x^2) *(1-x+x^2) / (1-x+x^3-x^4+x^5-x^7+x^8). - R. J. Mathar, Apr 09 2011
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EXAMPLE
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1 - x^3 - x^5 - x^6 + x^8 + x^9 + x^11 - x^14 + x^15 - x^18 - x^20 + ...
q - q^7 - q^11 - q^13 + q^17 + q^19 + q^23 - q^29 + q^31 - q^37 - q^41 + ...
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PROG
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(PARI) {a(n) = kronecker( -60, 2*n + 1)}
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CROSSREFS
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Sequence in context: A010059 A143580 A011749 * A104105 A143221 A126999
Adjacent sequences: A188575 A188576 A188577 * A188579 A188580 A188581
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Apr 04 2011
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STATUS
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approved
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