A226728 - OEIS

%I #30 Aug 16 2013 03:55:23

%S 1,-1,0,0,0,1,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,-1,0,0,0,1,0,0,0,-1,0,0,

%T 0,0,0,0,0,1,0,0,0,-2,0,0,0,3,0,0,0,-2,0,0,0,0,0,0,0,2,0,0,0,-4,0,0,0,

%U 4,0,0,0,-3,0,0,0,1,0,0,0,3,0,0,0,-6,0,0,0,7,0,0,0,-5,0,0,0,0,0,0,0,5,0,0,0,-9,0

%N G.f.: 1/G(0), where G(k) = 1 + q^(k+1) / (1 - q^(k+1)/G(k+2) ).

%F G.f.: 1/(1+q/(1-q/(1+q^3/(1-q^3/(1+q^5/(1-q^5/(1+q^7/(1-q^7/(1+ ... ))))))))).

%F G.f.: 1/W(0), where W(k)= 1 + x^(2*k+1)/(1 - x^(2*k+1)/W(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Aug 16 2013

%o (PARI) N = 166;  q = 'q + O('q^N);

%o G(k) = if(k>N, 1, 1 + q^(k+1) / (1 - q^(k+1) / G(k+2) ) );

%o gf = 1 / G(0);

%o Vec(gf)

%Y Cf. A049346 (g.f.: 1 - 1/G(0), G(k)= 1 + q^(k+1) / (1 - q^(k+1)/G(k+1) ) ).

%Y Cf. A226729 (g.f.: 1/G(0), G(k) = 1 - q^(k+1) / (1 - q^(k+1)/G(k+2) ) ).

%Y Cf. A006958 (g.f.: 1/G(0), G(k) = 1 - q^(k+1) / (1 - q^(k+1)/G(k+1) ) ).

%Y Cf. A227309 (g.f.: 1/G(0), G(k) = 1 - q^(k+1) / (1 - q^(k+2)/G(k+1) ) ).

%K sign

%O 0,42

%A _Joerg Arndt_, Jun 29 2013