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%I #4 Jan 28 2021 21:41:11
%S 1,2,3,8,31,146,754,4168,24387,149878,961735,6413730,44305495,
%T 316289264,2329690081,17685913364,138276568051,1112831978494,
%U 9214885055084,78482008660596,687242245179732,6184901074959982,57179080181866903,542740440965244192
%N G.f. A(x) satisfies: A(x) = Sum_{n>=0} x^n/(1 - x*A(x)^(2*n)).
%C Equals row sums of triangle A340934.
%e G.f.: A(x) = 1 + 2*x + 3*x^2 + 8*x^3 + 31*x^4 + 146*x^5 + 754*x^6 + 4168*x^7 + 24387*x^8 + 149878*x^9 + 961735*x^10 + 6413730*x^11 + 44305495*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^(2*m) +x*O(x^n))) ); polcoeff(A, n)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A340934.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jan 28 2021
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