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%I #6 Jun 19 2022 12:30:35
%S 1,1,2,7,44,493,9974,372403,26247008,3559692121,942403603562,
%T 491777568765151,508938530329020692,1048381120745440503877,
%U 4307758467916752367544414,35349370769806113877653011083,579693879415731511179957972407624
%N a(n) = 1 + Sum_{k=1..n-1} binomial(n-1,k) * 2^(k-1) * a(k).
%F G.f. A(x) satisfies: A(x) = (2 - x + x * A(2*x/(1 - x))) / (2 * (1 - x)).
%p a:= proc(n) option remember; 1+add(a(k)*
%p binomial(n-1, k)*2^(k-1), k=1..n-1)
%p end:
%p seq(a(n), n=0..16); # _Alois P. Heinz_, Jun 19 2022
%t a[n_] := a[n] = 1 + Sum[Binomial[n - 1, k] 2^(k - 1) a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 16}]
%t nmax = 16; A[_] = 0; Do[A[x_] = (2 - x + x A[2 x/(1 - x)])/(2 (1 - x)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y Cf. A000110, A126443, A352859, A352860.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jun 19 2022
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