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A154955 a(1) = 1, a(2) = -1, followed by 0, 0, 0, ... . 13
1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Matrix inverse of A000012.
Moebius transform of the sequence A000035. Dirichlet inverse of A209229. Partial sums of a(n) is characteristic function of 1 (A063524). a(n)=(-1)^(n+1)*A019590(n). a(n) for n >= 1 is Dirichlet convolution of following functions b(n), c(n), a(n) = Sum_{d|n} b(d)*c(n/d): a(n) = A000012(n) * A092673(n). Examples of Dirichlet convolutions with function a(n), i.e. b(n) = Sum_{d|n} a(d)*c(n/d): a(n) * A000012(n) = A000035(n), a(n) * A000027(n) = A026741(n), a(n) * A008683(n) = A092673(n), a(n) * A036987(n-1) = A063524(n), a(n) * A000005(n) = A001227(n). - Jaroslav Krizek, Mar 21 2009
The Kn21 sums, see A180662, of triangle A108299 equal the terms of this sequence. - Johannes W. Meijer, Aug 14 2011
{a(n-1)}_{n>=1}, gives the alternating row sums of A132393. - Wolfdieter Lang, May 09 2017
With offset 0 the alternating row sums of A097805. - Peter Luschny, Sep 07 2017
LINKS
FORMULA
G.f.: A(x) = x - x^2 = x / (1 + x / (1 - x)). - Michael Somos, Jan 03 2013
a(n) = (2/sqrt(3))*sin((2*Pi/3)*n!). - Lorenzo Pinlac, Jan 16 2022
PROG
(PARI) A154955(n)=(n==1)-(n==2) \\ M. F. Hasler, Jan 13 2012
CROSSREFS
Cf. A132393.
Sequence in context: A060576 A261012 A019590 * A240356 A240354 A240352
KEYWORD
sign,easy
AUTHOR
Mats Granvik, Jan 18 2009
STATUS
approved

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Last modified April 21 12:42 EDT 2024. Contains 371870 sequences. (Running on oeis4.)