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G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x) - x^2*A(x)/(1 - 2*x*A(x) - 2*x^2*A(x)/(1 - 3*x*A(x) - 3*x^2*A(x)/(1 - ...)))), a continued fraction.
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%I #4 Mar 21 2018 08:01:02

%S 1,1,3,11,47,221,1115,5947,33231,193453,1169239,7322827,47479855,

%T 318661109,2214609419,15948123771,119101155215,923085573061,

%U 7428862280327,62094175343547,538956428549743,4854974080968669,45347892277523467,438688081755797051,4389356528040108847

%N G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x) - x^2*A(x)/(1 - 2*x*A(x) - 2*x^2*A(x)/(1 - 3*x*A(x) - 3*x^2*A(x)/(1 - ...)))), a continued fraction.

%e G.f. A(x) = 1 + x + 3*x^2 + 11*x^3 + 47*x^4 + 221*x^5 + 1115*x^6 + 5947*x^7 + 33231*x^8 + ...

%Y Cf. A000110, A088368.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 20 2018