%I #6 May 13 2018 20:19:29
%S 0,1,1,2,5,15,51,191,773,3338,15243,73131,366815,1916260,10394665,
%T 58404853,339223859,2033188222,12556915219,79807729238,521399203037,
%U 3497978659977,24076009827669,169865542733652,1227553152971419,9079751310622581,68692742886823205
%N G.f. satisfies: A(x) = 1 / (1/x - 1 - A(A(x))), with A(0) = 0.
%F a(n) = A193296(n+1) if n>0.
%e G.f. = x + x^2 + 2*x^3 + 5*x^4 + 15*x^5 + 51*x^6 + 191*x^7 + 773*x^8 + 3338*x^9 + ...
%t a[ n_] := If[n < 0, 0, SeriesCoefficient[ Nest[ 1 / (1/x - 1 - (# /. x -> #)) &, O[x], Ceiling[n/2]], {x, 0, n}]];
%o (PARI) {a(n) = my(A); if( n<0, 0, A = O(x); forstep(k=1, n, 2, A = 1 / (1/x - 1 - subst(A, x, A))); polcoeff(A, n))};
%Y Cf. A193296.
%K nonn
%O 0,4
%A _Michael Somos_, May 12 2018