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G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x)/(1 - x*A(x)/(1 - x^2*A(x)/(1 - x^2*A(x)/(1 - x^3*A(x)/(1 - x^3*A(x)/(1 - ...))))))), a continued fraction.
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%I #4 Mar 21 2018 08:01:22

%S 1,1,3,11,46,205,957,4614,22803,114898,588052,3048612,15975922,

%T 84489890,450363757,2417104782,13050778500,70841037919,386357165119,

%U 2116097719571,11634392901981,64188480019008,355255552604237,1971866447509917,10973973061151433,61222237473973758

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

%e G.f. A(x) = 1 + x + 3*x^2 + 11*x^3 + 46*x^4 + 205*x^5 + 957*x^6 + 4614*x^7 + 22803*x^8 + 114898*x^9 + ...

%Y Cf. A006958, A088368, A192728.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 20 2018