%I #7 Jan 27 2021 10:50:11
%S 1,2,3,6,16,52,189,740,3067,13330,60366,283504,1376000,6884364,
%T 35440060,187471028,1018049493,5671511886,32396788157,189673021414,
%U 1137795705447,6991058047594,43984892028735,283267507353084,1866622184589906
%N G.f. A(x) satisfies: A(x) = Sum_{n>=0} x^n/(1 - x*A(x)^n).
%C Equals row sums of triangle A340910.
%e G.f.: A(x) = 1 + 2*x + 3*x^2 + 6*x^3 + 16*x^4 + 52*x^5 + 189*x^6 + 740*x^7 + 3067*x^8 + 13330*x^9 + 60366*x^10 + 283504*x^11 + 1376000*x^12 + ...
%e where
%e A(x) = 1/(1-x) + x/(1 - x*A(x)) + x^2/(1 - x*A(x)^2) + x^3/(1 - x*A(x)^3) + x^4/(1 - x*A(x)^4) + x^5/(1 - x*A(x)^5) + ...
%o (PARI) {a(n) = my(A=1); for(i=1,n, A = sum(m=0,n, x^m/(1 - x*A^m +x*O(x^n))) ); polcoeff(A,n)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A340910.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jan 26 2021