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A188578 Expansion of (1 - x^3) * (1 - x^5) * (1 - x^6) / (1 - x^15) in powers of x. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..104.

M. Somos, Rational Function Multiplicative Coefficients

FORMULA

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

EXAMPLE

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 + ...

PROG

(PARI) {a(n) = kronecker( -60, 2*n + 1)}

CROSSREFS

Sequence in context: A010059 A143580 A011749 * A104105 A143221 A126999

Adjacent sequences:  A188575 A188576 A188577 * A188579 A188580 A188581

KEYWORD

sign

AUTHOR

Michael Somos, Apr 04 2011

STATUS

approved

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Last modified July 24 04:27 EDT 2014. Contains 244874 sequences.