%I #11 Nov 03 2021 12:39:08
%S 1,3,15,123,1623,35427,1349727,94653195,12690736167,3325408581747,
%T 1722610175806383,1774299723226774683,3644417103927252697335,
%U 14949404433893216347632003,122555228634241017164802041343,2008680242472430855727593100321067
%N G.f. A(x) satisfies: A(x) = 1 / (1 - 2*x - x * A(2*x)).
%F a(n) ~ c * 2^(n*(n-1)/2), where c = 6*Product_{j>=1} (2^j+1)/(2^j-1) = 49.5359276146695003932648450...
%F a(0) = 1; a(n) = 2 * a(n-1) + Sum_{k=0..n-1} 2^k * a(k) * a(n-k-1). - _Ilya Gutkovskiy_, Nov 03 2021
%t nmax = 20; A[_] = 0; Do[A[x_] = 1/(1 - 2*x - x*A[2*x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y Cf. A348857, A348860, A348875, A348901, A348904.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Nov 03 2021