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%I #23 Jan 25 2020 00:54:31
%S 1,2,6,26,142,898,6342,49114,412046,3711746,35660166,363484058,
%T 3914162830,44370673282,527868672582,6572992645978,85461951576974,
%U 1157778354181634,16310949128381190,238543136307926810
%N Expansion of (A(x)-1)/(x*A(x)), A(x) the g.f. of A004211.
%C Hankel transform is A108400.
%F G.f.: 1/(1-2x/(1-x/(1-4x/(1-x/(1-6x/(1-x/(1-8x/(1-x/(1-... (continued function).
%F a(n) = Sum_{k=0..n} A086329(n,k)*2^k. - _Philippe Deléham_, Dec 05 2009
%F G.f.: 1/U(0) where U(k) = 1 - x - 2*x*k + x*(2*x*k + 2*x - 1)/U(k+1); (continued fraction, Euler's 1st kind, 1-step). - _Sergei N. Gladkovskii_, Sep 24 2012
%F G.f.: 1/x - 1/( x*G(0) - 1 ) where G(k) = 1 - (4*x*k-1)/(x - x^4/(x^3 - (4*x*k-1)*(4*x*k+2*x-1)*(4*x*k+4*x-1)/G(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Jan 08 2013
%F G.f.: (1 - G(0))/x where G(k) = 1 - x/(1 - 2*x*(k + 1)/G(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Jan 30 2013
%F G.f.: 1/x + 1 - (2*x+1)/(G(0) + 2*x+1), where G(k)= 2*x*k - x - 1 - 2*(k+1)*x^2/G(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Jul 21 2013
%F G.f.: 1/x - Q(0)/x, where Q(k) = 1 - x*(2*k+1) - (2*k+2)*x^2/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Oct 09 2013
%K easy,nonn
%O 0,2
%A _Paul Barry_, Dec 04 2009
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