%I A000007 M0002
%S A000007 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,
%T A000007 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,
%U A000007 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 A000007 The characteristic function of 0: a(n) = 0^n.
%C A000007 Changing the offset to 1 gives the arithmetical function a(1)=1, a(n)=0 
               for n>1, the identity function for Dirichlet multiplication (see 
               Apostol).
%C A000007 Hankel transform (see A001906 for definition) of : A000007 (powers of 
               0), A000012 (powers of 1), A000079 (powers of 2), A000244 (powers 
               of 3), A000302 (powers of 4), A000351 (powers of 5), A000400 (powers 
               of 6), A000420 (powers of 7), A001018 (powers of 8), A001019 (powers 
               of 9), A011557 (powers of 10), A001020 (powers of 11), etc. ... - 
               Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 07 2005
%C A000007 This is the identity sequence with respect to convolution. - David W. 
               Wilson (davidwwilson(AT)comcast.net), Oct 30 2006
%C A000007 a(A000004(n)) = 1; a(A000027(n)) = 0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 12 2008]
%C A000007 (1+(-1)^nth prime)/2. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 25 2009]
%D A000007 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 
               1976, page 30.
%D A000007 Paul Barry, A Catalan Transform and Related Transformations on Integer 
               Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
%D A000007 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000007 David Wasserman, <a href="b000007.txt">Table of n, a(n) for n = 0..1000</
               a>
%H A000007 Daniele A. Gewurz and Francesca Merola, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">Sequences realized as Parker vectors ...</
               a>, J. Integer Seqs., Vol. 6, 2003.
%H A000007 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%H A000007 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a>
%F A000007 Multiplicative with a(p^e) = 0. - David W. Wilson, Sep 01, 2001
%F A000007 a(n)= floor(1/(n+1)). - Franz Vrabec (franz.vrabec(AT)aon.at), Aug 24 
               2005
%F A000007 a(n)=((n+1)!^2 mod (n+2))*((n+2)!^2 mod (n+3)), with n>=0 - Paolo P. 
               Lava (ppl(AT)spl.at), Apr 24 2007
%F A000007 a(n)=1-{[(n+1)!+1] mod (n+1)}, with n>=0. - Paolo P. Lava (ppl(AT)spl.at), 
               May 22 2007
%F A000007 a(n)=1-[(n+2) mod (n+1)], with n>=0. - Paolo P. Lava (ppl(AT)spl.at), 
               Jun 27 2007
%F A000007 a(n)=C(2*n,n) mod 2 - Paolo P. Lava (ppl(AT)spl.at), Aug 31 2007
%F A000007 a(n)=((-1)^A000040(n)+1)/2. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 25 2009]
%p A000007 A000007 := proc(n) if n = 0 then 1 else 0; fi; end;
%p A000007 with(combstruct); spec := [A, {A=Z} ]; [seq(combstruct[count](spec,size=n),
               n=1..20)];
%t A000007 a[n_] := If[n == 0, 1, 0]
%o A000007 (PARI) a(n)=!n; for(n=0,100,print1(a(n)","))
%o A000007 (MAGMA) [1] cat [0:n in [1..100]]; - from Sergei Haller (sergei(AT)sergei-haller.de), 
               Dec 21 2006
%Y A000007 Cf. A063524.
%Y A000007 Cf. A000040. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 
               25 2009]
%Y A000007 Sequence in context: A062157 A112347 A134824 this_sequence A014041 A015868 
               A015824
%Y A000007 Adjacent sequences: A000004 A000005 A000006 this_sequence A000008 A000009 
               A000010
%K A000007 core,easy,nonn,mult
%O A000007 0,1
%A A000007 N. J. A. Sloane (njas(AT)research.att.com).