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%I #45 Dec 31 2023 10:22:26
%S 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,
%T 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,
%U 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
%N a(1) = 1, a(2) = -1, followed by 0, 0, 0, ... .
%C Matrix inverse of A000012.
%C 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
%C The Kn21 sums, see A180662, of triangle A108299 equal the terms of this sequence. - _Johannes W. Meijer_, Aug 14 2011
%C {a(n-1)}_{n>=1}, gives the alternating row sums of A132393. - _Wolfdieter Lang_, May 09 2017
%C With offset 0 the alternating row sums of A097805. - _Peter Luschny_, Sep 07 2017
%F G.f.: A(x) = x - x^2 = x / (1 + x / (1 - x)). - _Michael Somos_, Jan 03 2013
%F a(n) = (2/sqrt(3))*sin((2*Pi/3)*n!). - _Lorenzo Pinlac_, Jan 16 2022
%o (PARI) A154955(n)=(n==1)-(n==2) \\ _M. F. Hasler_, Jan 13 2012
%Y Cf. A000035, A036987, A063524, A019590, A000012, A000027, A026741, A008683, A092673, A000005, A001227. - _Jaroslav Krizek_, Mar 21 2009
%Y Cf. A132393.
%K sign,easy
%O 1,1
%A _Mats Granvik_, Jan 18 2009
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